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Measurement & Math Tools
Units, dimensions, errors, vectors and the maths every physicist needs. 49 topics, from beginner to advanced. Open the interactive version with labs and quizzes
Every physics problem starts with measurement: deciding what to measure, what units to use, and how precise the answer should be. This area covers the base units of the SI system, unit prefixes, scientific notation, significant figures, and how to estimate and report errors. It also introduces the vector and graph skills you will need throughout the rest of the subject.
How the topics connect
Measurement and maths come first because every later area uses the same tools: units to check answers, vectors to describe forces and velocities, graphs to read experiments, and error analysis to judge whether two results really disagree. Learn the units and the vector rules here, and the rest of the subject becomes much easier to follow.
Real-world uses
Choose the right instrument, such as a vernier calliper or micrometer screw gauge, and report a reading with the correct number of significant figures.
Use dimensional analysis to catch a wrong formula before you finish the calculation, for example by confirming that both sides of an equation have units of energy.
Quote results with uncertainties and units in the form scientists and engineers expect.
Convert between units and prefixes quickly when reading specifications, recipes or fuel economy figures.
Choose instruments with the right precision, repeat readings and estimate the uncertainty before you collect any data.
Understand how results are quoted with error bars, significant figures and units, so you can judge how strong a claim really is.
What is physics?
The science of matter, energy, space and time and how they interact.
Physics looks for the few simple rules behind a huge range of phenomena, from a falling apple to a galaxy. It works by a loop: observe, propose a model, make a numerical prediction, test it by experiment, and revise. A theory is only useful if it can be proved wrong by a measurement, which is why physics leans so heavily on numbers and units.
Newton's gravity predicted the return of Halley's comet decades in advance. The prediction was specific enough to fail, and it did not.
Physics is not just memorising formulas. Each formula is a compact summary of a model with limits, so always ask where it stops being valid.
Physical quantity
Anything measurable, expressed as a number times a unit.
A physical quantity is a property you can measure, written as a number together with a unit. The number alone is meaningless: "5" could be seconds, metres or newtons. Quantities are either base (chosen as independent, such as length and time) or derived (built by combining base ones, such as speed).
A car travels 90 km in 1.5 h. The quantity is a distance of 90 km, a time of 1.5 h, and the derived quantity speed is 60 km/h.
Never drop units in intermediate steps. Carrying them through is the cheapest error check you have.
SI base units
Seven base units: metre, kilogram, second, ampere, kelvin, mole, candela.
The International System (SI) fixes seven base units: metre (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount) and candela (luminous intensity). Since 2019 all seven are defined from fixed values of natural constants, such as the speed of light and Planck's constant, so any lab can reproduce them without a physical artefact.
The metre is the distance light travels in 1/299,792,458 of a second, so the speed of light is exactly 299,792,458 m/s by definition.
Grams are not the SI base unit of mass; the kilogram is. This matters when you substitute into formulas like F = ma.
Derived units
Units built from base units, such as newton = kg·m/s².
N = kg·m·s⁻²Derived units are products and quotients of base units. Many have their own names to save writing: newton for force, joule for energy, watt for power, pascal for pressure. Knowing the base-unit form lets you check any equation.
Pressure is force over area, so 1 Pa = 1 N/m² = 1 kg·m⁻¹·s⁻². Energy 1 J = 1 N·m = 1 kg·m²·s⁻².
Mixing a derived unit with the wrong prefix, such as using kN as N, gives answers off by a thousand. Convert first.
Prefixes (milli, kilo, mega)
Powers of ten shorthand for very large or small values.
k=10³, m=10⁻³, μ=10⁻⁶Prefixes are powers of ten attached to units so numbers stay readable: nano 10⁻⁹, micro 10⁻⁶, milli 10⁻³, kilo 10³, mega 10⁶, giga 10⁹. They change the size of the unit, not the physical quantity.
A 2.5 GHz processor runs at 2.5×10⁹ cycles per second. A 450 nm light wave has wavelength 4.5×10⁻⁷ m.
Squares and cubes of prefixed units multiply the factor: 1 cm² = 10⁻⁴ m², not 10⁻² m².
Scientific notation
Writing numbers as a×10ⁿ to handle very large or small values.
a × 10ⁿScientific notation writes a number as a × 10ⁿ with 1 ≤ a < 10. It makes huge and tiny values easy to compare (just look at the exponent) and to multiply: add the exponents, multiply the leading numbers.
(3×10⁸)×(2×10⁻³) = 6×10⁵. Dividing 6×10⁵ by 2×10² gives 3×10³.
When adding numbers, first give them the same exponent. 2×10³ + 5×10² is 2.5×10³, not 7×10⁵.
Length measurement
Rulers, vernier callipers and screw gauges measure lengths at different precision.
Different instruments suit different precisions: a ruler reads to about 1 mm, a vernier calliper to 0.1 mm or 0.05 mm, and a screw gauge to 0.01 mm. For large distances physicists use indirect methods such as parallax or timing a reflected signal.
To find the thickness of one sheet of paper, measure a stack of 200 sheets and divide. Repeating a measurement over many units reduces relative error.
Reading a scale at an angle gives parallax error. Always view the pointer directly from above.
Vernier calliper
A sliding scale that reads to a fraction of the smallest main-scale division.
LC = 1 MSD − 1 VSDA vernier has a main scale and a sliding scale whose divisions are slightly shorter. The smallest reading, the least count, is the difference between one main division and one vernier division. The reading is the main-scale value just before the zero of the vernier plus (matching vernier line × least count).
Main scale in mm, 10 vernier divisions equal 9 main divisions, so LC = 1 − 0.9 = 0.1 mm. If the main reading is 23 mm and the 6th vernier line matches, the length is 23 + 0.6 = 23.6 mm.
Check for zero error with the jaws closed and subtract it from every reading.
Screw gauge
Micrometer using a screw thread to measure small thicknesses.
LC = pitch / circular divisionsA screw gauge turns a precision screw so one full rotation advances the spindle by the pitch (often 0.5 or 1 mm). The circular scale divides the pitch, giving a least count = pitch ÷ number of circular divisions. Reading = main (linear) scale + circular scale × LC.
Pitch 0.5 mm, 50 circular divisions: LC = 0.01 mm. Linear 3.5 mm and circular 27 give 3.5 + 0.27 = 3.77 mm.
Always stop tightening with the ratchet to avoid squeezing the object, and correct for zero error, which can be positive or negative.
Measuring time
Clocks, stopwatches and atomic oscillations define the second.
Time is measured by counting a regular repeating process: a pendulum swing, a quartz crystal vibration, or an atomic transition. The second is defined by 9,192,631,770 oscillations of caesium-133 radiation. Human reaction time of roughly 0.2 s limits stopwatch accuracy.
Timing 20 swings of a pendulum and dividing by 20 gives the period with 20 times less relative error than timing one swing.
Start counting at zero, not one, when you start the watch on a swing, otherwise you count one extra period.
Mass vs weight
Mass is the amount of matter; weight is the gravitational force on it.
W = mgMass measures how much matter a body contains and how strongly it resists acceleration; it is the same everywhere. Weight is the gravitational force on that mass and varies with place: W = mg. A balance compares masses, while a spring scale measures weight.
A 60 kg person weighs about 589 N on Earth (g = 9.81) but only about 98 N on the Moon (g ≈ 1.63), yet their mass is still 60 kg.
Everyday "weight in kg" really means mass. In physics equations, use newtons for weight.
Significant figures
Digits that carry meaning in a measurement.
Significant figures are the digits that carry information about a measurement's precision. Non-zero digits count; zeros between digits count; leading zeros do not; trailing zeros count only if there is a decimal point or they are written in scientific notation.
0.00450 has three sig figs (4, 5, 0). 1200 may have two, three or four; writing 1.20×10³ makes it three.
Do not keep every calculator digit. The final answer cannot be more precise than the least precise input.
Rounding rules
Results should not be reported with more precision than the inputs.
In multiplication and division, round the result to the fewest significant figures of any input. In addition and subtraction, round to the fewest decimal places. Keep an extra digit in intermediate steps and round only at the end.
12.11 + 0.3 = 12.4 (one decimal place). 4.56 × 1.4 = 6.4 (two sig figs).
Rounding early and repeatedly compounds small errors and can shift the final digit.
Accuracy vs precision
Accuracy is closeness to truth; precision is repeatability.
Accuracy is how close a result is to the true value. Precision is how close repeated results are to each other. A scale that always reads 0.5 kg too high is precise but not accurate, and a scale that scatters around the correct value is accurate on average but not precise.
Darts all clustered in the top left of the board: precise, not accurate. Darts scattered evenly around the bullseye: accurate on average, not precise.
Averaging many readings improves precision but cannot remove a systematic offset.
Systematic error
A consistent bias from instruments or method, repeated every measurement.
A systematic error shifts all measurements in the same direction by the same kind of cause: a mis-calibrated instrument, a zero error, or a flawed method. It cannot be reduced by repeating the same experiment; you must find and correct the cause, for example by calibrating against a known standard.
A stopwatch that runs 1% fast makes every measured time 1% too long, however many trials you take.
Good precision can hide a systematic error, because the results agree with each other and look trustworthy.
Random error
Unpredictable scatter that averages out with repeated readings.
Random errors vary unpredictably from reading to reading, due to reaction time, tiny fluctuations or reading estimates. They scatter above and below the true value, so averaging n readings reduces the uncertainty of the mean by about √n.
Ten timings of a swing might read 2.1, 2.3, 2.2, 2.0, 2.2 s. The mean 2.16 s is more reliable than any single value.
Averaging does not help if you keep making the same mistake, since that is systematic.
Absolute error
Magnitude of the difference between measured and true value.
Δa = ∣a_measured − a_true∣Absolute error is the size of the difference between a measured value and the true (or mean) value, in the same units as the measurement. It tells how far off you are but not how serious that is relative to the size of the quantity.
True length 50.0 cm, measured 49.6 cm: absolute error = 0.4 cm.
An error of 1 cm is huge for a pencil but negligible for a road. Use relative error to compare.
Relative and percent error
Absolute error divided by the measured value.
δ = Δa / aRelative error is absolute error divided by the measured value; multiply by 100 for a percentage. It shows how significant the error is and lets you compare measurements of different sizes.
0.4 cm error on 50.0 cm gives relative error 0.008 or 0.8%.
Use the true or best-estimate value in the denominator, not the error itself.
Error in a sum or difference
Absolute errors add when quantities are added or subtracted.
Δ(A±B) = ΔA + ΔBWhen quantities are added or subtracted, their absolute errors add (worst case). For Z = A ± B, ΔZ = ΔA + ΔB. Subtraction does not cancel errors, which is why subtracting two nearly equal measured numbers is risky.
Two lengths 10.0 ± 0.1 cm and 4.0 ± 0.1 cm: sum 14.0 ± 0.2 cm, difference 6.0 ± 0.2 cm.
Errors never subtract. A common slip is to write ΔZ = ΔA − ΔB.
Error in product or quotient
Relative errors add when quantities are multiplied or divided.
Δz/z = ΔA/A + ΔB/BFor Z = AB or A/B the relative errors add: ΔZ/Z = ΔA/A + ΔB/B. Express each error as a fraction first, then convert the total back to an absolute error if needed.
A = 5.0 ± 0.1 (2%) and B = 2.0 ± 0.1 (5%): AB = 10.0 with 7% error, i.e. 10.0 ± 0.7.
Do not add absolute errors when multiplying; the units differ.
Error in powers
Relative error is multiplied by the exponent.
Δz/z = n·ΔA/AIf Z = Aⁿ the relative error is multiplied by the exponent: ΔZ/Z = n·ΔA/A. For several factors, each term contributes |exponent| times its relative error, so quantities raised to high powers dominate the uncertainty.
A sphere radius measured to 1% gives volume (r³) with 3% error and area (r²) with 2% error.
The exponent can be negative or fractional, but the contribution to the error is always added, using its absolute value.
Mean and standard deviation
Statistics describing the centre and spread of repeated measurements.
σ = √(Σ(x−x̄)²/(n−1))The mean x̄ is the best estimate of the true value from repeated readings. The standard deviation σ measures the typical scatter of individual readings, and σ/√n, the standard error, measures how well the mean is known. Report results as x̄ ± standard error.
Readings 9.8, 9.9, 10.1, 10.2: mean 10.0, deviations −0.2, −0.1, 0.1, 0.2, σ ≈ 0.18.
Standard deviation does not shrink with more data; the standard error of the mean does.
Dimensions of a quantity
Expression of a quantity in powers of base dimensions M, L, T.
[F] = M L T⁻²The dimension of a quantity states how it is built from base dimensions: mass [M], length [L], time [T] and others. It ignores units and numbers. Velocity is [L T⁻¹], acceleration [L T⁻²], force [M L T⁻²], energy [M L² T⁻²].
Pressure = force/area has dimensions M L T⁻² / L² = M L⁻¹ T⁻².
Dimensions are not the same as units: metres and feet differ in unit but share the dimension [L].
Dimensional homogeneity
Every term in a valid equation has the same dimensions.
Only quantities with the same dimensions can be added, subtracted or equated. Every term in a physical equation must therefore have identical dimensions. Arguments of sine, exponential and log must be dimensionless.
In s = ut + ½at², each term is [L]: ut is (L/T)·T, and at² is (L/T²)·T².
The equation x = sin(t) is dimensionally invalid because t has units; it must be sin(ωt) with ω in 1/time.
Checking equations by dimensions
Dimensional analysis can reject (not prove) a formula.
To test a formula, write the dimensions of each side. If they differ, the formula is definitely wrong. If they match, it may still be wrong by a numerical factor or have the wrong structure.
Is T = 2π√(g/L) valid? √(g/L) has dimension T⁻¹, not T, so no. The correct one is √(L/g).
Matching dimensions is necessary but not sufficient. v = ½ at passes, and so does v = 5at.
Deriving formulas by dimensions
Use dimensions to find how a quantity depends on others, up to a constant.
T ∝ √(l/g)Assume a quantity depends on a product of powers of the relevant variables, then choose the exponents so the dimensions match. This gives the functional form but not the constant.
For a pendulum, guess T = k·m^a l^b g^c. Matching [T] gives a = 0, b = ½, c = −½, so T = k√(l/g).
You must include every variable that matters. Leaving one out gives a wrong result without any warning.
Limitations of dimensional analysis
It cannot find dimensionless constants or handle sums of functions.
Dimensional analysis cannot find dimensionless constants (like 2π or ½), cannot handle sums or trig and exponential functions of variables, and fails if there are more variables than independent dimensions without extra information. It also cannot tell whether a variable truly matters.
It gives the period of a pendulum up to a constant but cannot say that large amplitudes change the period.
Use it as a sanity check and a way to guess scaling, then confirm with theory or experiment.
Dimensionless numbers
Ratios such as Reynolds or Mach numbers that govern similarity.
Dimensionless numbers are ratios where all units cancel. They determine how a system behaves independent of size or units. Examples: Reynolds number (inertia vs viscosity), Mach number (speed vs sound speed), the fine-structure constant (≈1/137).
Flow in a pipe turns turbulent when the Reynolds number Re = ρvd/η exceeds a few thousand, regardless of the fluid.
Two systems with the same dimensionless numbers behave alike, which is why scale models of ships and aircraft work.
Order-of-magnitude estimates
Fermi estimation gives quick answers to within a factor of ten.
An estimate to within a power of ten, built from rough numbers and simple reasoning (Fermi estimation). The goal is a plausible magnitude, so you can sense-check calculations or see whether an idea is feasible.
How many piano tuners are in a city of 3 million? About one piano per 100 people gives 30,000 pianos, each tuned once a year, a tuner does about 1,000 a year, so roughly 30 tuners.
Don't chase decimals here. The goal is the exponent.
Unit conversion
Multiply by ratios equal to one to change units.
Multiply by conversion factors written as fractions equal to one so the unwanted units cancel. This works for compound units too, but powers need care.
72 km/h = 72 × (1000 m / 1 km) × (1 h / 3600 s) = 20 m/s.
Convert squared or cubed units by squaring or cubing the factor. 1 m³ = 10⁶ cm³, not 100.
Scalars and vectors
Scalars have magnitude only; vectors have magnitude and direction.
A scalar has magnitude only (mass, time, temperature, energy). A vector has magnitude and direction and obeys vector addition (displacement, velocity, force). Direction matters, so equal magnitudes do not make two vectors equal.
Walking 3 km east then 3 km west gives distance 6 km but displacement 0.
Speed is a scalar, velocity is a vector. Average speed and the magnitude of average velocity can differ.
Vector representation
Arrows with length for magnitude and direction for orientation.
Draw a vector as an arrow: its length is proportional to magnitude and the arrowhead shows direction. Written as bold letters or with a bar. A vector can be moved without changing it as long as length and direction stay the same.
A force of 10 N at 30° above the x-axis is drawn as an arrow 10 units long inclined at 30°.
Angles must be measured from a stated reference axis; otherwise the same drawing can mean different things.
Vector addition
Add vectors head-to-tail or by components.
R = A + BTo add vectors geometrically, place the tail of the second at the head of the first; the sum runs from the first tail to the last head. Algebraically, add like components: (Ax+Bx, Ay+By). Addition is commutative and associative.
A = (3, 1), B = (2, 4): A + B = (5, 5), magnitude √50 ≈ 7.07.
Magnitudes do not add unless the vectors point the same way. |A + B| ≤ |A| + |B|.
Parallelogram law
Resultant is the diagonal of the parallelogram built on two vectors.
R² = A²+B²+2AB cosθTwo vectors from the same point form the sides of a parallelogram; the diagonal from that point is their resultant. Its magnitude is R = √(A² + B² + 2AB cosθ), with θ the angle between them. It is the same as head-to-tail addition.
Forces 3 N and 4 N at 90°: R = √(9+16) = 5 N. At 0° they give 7 N; at 180°, 1 N.
θ is the angle between the tails when both start at the same point, not the exterior angle.
Vector components
Resolve a vector into perpendicular parts along chosen axes.
Ax = A cosθ, Ay = A sinθAny vector can be split into perpendicular parts along chosen axes: Ax = A cosθ and Ay = A sinθ, where θ is measured from the x-axis. This turns vector problems into simple algebra on each axis.
A 50 N pull at 37° above horizontal has horizontal component 40 N and vertical component 30 N.
Which of sin and cos goes with which axis depends on where θ is measured from. Always check with the limiting cases θ = 0 and 90°.
Unit vectors
Vectors of length one giving direction: i, j, k.
A = Axî + Ayĵ + Azk̂Unit vectors have length 1 and show direction only: î, ĵ, k̂ along x, y, z. Any vector is A = Axî + Ayĵ + Azk̂. Dividing a vector by its magnitude gives its unit vector.
The vector (3, 4) has magnitude 5 and unit vector (0.6, 0.8).
The hat tells you it carries no units; the magnitude carries the units.
Dot product
Scalar product measuring how much two vectors align.
A·B = AB cosθThe dot (scalar) product A·B = AB cosθ = AxBx + AyBy + AzBz gives a scalar. It measures how much one vector points along the other, and is zero for perpendicular vectors. Work is a dot product: W = F·d.
A force (2, 3) N acting over a displacement (4, 0) m does W = 8 J.
The result is a number, not a vector, and the order does not matter.
Cross product
Vector product perpendicular to both, magnitude equals parallelogram area.
∣A×B∣ = AB sinθThe cross (vector) product A×B has magnitude AB sinθ and a direction perpendicular to both, given by the right-hand rule. It is largest for perpendicular vectors and zero for parallel ones. Torque τ = r×F and magnetic force qv×B are cross products.
î × ĵ = k̂. A force of 10 N perpendicular to a 0.5 m wrench gives torque 5 N·m along the axis of the bolt.
The order matters: A×B = −(B×A).
Triple products
Scalar triple product gives the volume of a parallelepiped.
A·(B×C)The scalar triple product A·(B×C) equals the volume of the parallelepiped spanned by the three vectors and is zero if they lie in one plane. The vector triple product obeys A×(B×C) = B(A·C) − C(A·B).
For î, ĵ, k̂ the triple product is 1: a unit cube.
Brackets matter: A×(B×C) is different from (A×B)×C.
Calculus: derivatives
The rate of change of one quantity with respect to another.
v = dx/dtA derivative is the instantaneous rate of change: the slope of the tangent to a graph. In physics, velocity is the derivative of position and acceleration the derivative of velocity. Useful rules: d(xⁿ)/dt = nxⁿ⁻¹, d(sin ωt)/dt = ω cos ωt.
If x = 5t², then v = 10t and a = 10 m/s².
A derivative needs the quantity as a function of the variable; derivative with respect to time differs from with respect to position.
Calculus: integrals
Accumulating small contributions, the area under a curve.
x = ∫ v dtAn integral adds up many small pieces: the area under a curve. It undoes differentiation, so position is the integral of velocity and work is the integral of force over distance.
For constant acceleration a, ∫a dt = at + v₀ gives velocity, and integrating again gives x = x₀ + v₀t + ½at².
Definite integrals need limits; indefinite integrals need a constant, which is set by initial conditions.
Partial derivatives
Rate of change with respect to one variable holding others fixed.
∂f/∂xA partial derivative ∂f/∂x measures how f changes with x while all other variables are held fixed. It is used when a quantity depends on several variables, like temperature depending on position and time.
If f = x²y then ∂f/∂x = 2xy and ∂f/∂y = x².
Holding "the rest fixed" matters: ∂/∂x is not the same as the total derivative if other variables also change with x.
Gradient, divergence, curl
Vector calculus operators describing fields.
∇f, ∇·F, ∇×FWith the operator ∇ = (∂/∂x, ∂/∂y, ∂/∂z): the gradient ∇f points uphill in the direction of steepest increase of f; the divergence ∇·F measures how much a field spreads out from a point; the curl ∇×F measures local rotation. Maxwell's equations are written with them.
The electric field is E = −∇V; its divergence is ρ/ε₀: charge is the source of the field.
Gradient takes a scalar to a vector; divergence takes a vector to a scalar; curl takes a vector to a vector.
Differential equations in physics
Most laws are equations linking a quantity to its rates of change.
d²x/dt² = −ω²xMany laws say how a quantity changes in terms of itself, such as d²x/dt² = −ω²x. Solving means finding functions that satisfy the equation, then using initial conditions to fix constants. Exponentials describe growth and decay and sinusoids describe oscillation.
Radioactive decay dN/dt = −λN gives N = N₀e^{−λt}.
The solution is a family; you need initial or boundary conditions to choose one.
Taylor series and small angles
Approximate functions near a point, e.g. sinθ ≈ θ.
sinθ ≈ θ − θ³/6A smooth function near a point can be approximated by a polynomial: sinθ ≈ θ − θ³/6, cosθ ≈ 1 − θ²/2, (1+x)ⁿ ≈ 1 + nx. For small angles in radians, sinθ ≈ tanθ ≈ θ, which turns hard nonlinear equations into solvable ones, such as the small-angle pendulum.
At θ = 0.1 rad, sinθ = 0.09983, only 0.17% less than θ.
Angles must be in radians, and the approximation fails for larger angles; at 30° the error is about 4.5%.
Complex numbers and phasors
Represent oscillations as rotating vectors in the complex plane.
e^{iθ} = cosθ + i sinθComplex numbers z = a + ib with i² = −1 can be written as r e^{iθ}. Euler's formula e^{iθ} = cosθ + i sinθ links them to oscillations: a rotating arrow (phasor) projects onto a sinusoid. This simplifies adding oscillations and solving AC circuits.
Adding two AC voltages of the same frequency is just adding their phasors as vectors.
Only the real part (or imaginary part) of the complex expression represents the physical quantity.
Graphs and slopes
The slope of a graph gives a rate; the area under it gives an accumulated total.
A graph shows how one quantity depends on another. The slope gives the rate of change (units: y per x) and the area under it gives the accumulated product. Straight lines indicate proportionality; curves show nonlinear relations.
On a velocity–time graph the slope is acceleration and the area is displacement.
Check axis labels and scales before reading slopes. A steep line on a zoomed axis may be gentle in reality.
Curve fitting and linearisation
Plot y against a transformed x to get a straight line and read constants.
Experimental data are easier to analyse when plotted so the expected relation becomes a straight line y = mx + c, then slope and intercept give physical constants. For T = 2π√(L/g), plot T² against L: slope = 4π²/g.
Measure T for several lengths, plot T² vs L, and get g = 4π²/slope.
Fit the best line through the points, not the origin or the first and last points, and use error bars.
Logarithmic scales
Log axes turn power laws into straight lines.
A log axis spaces values by powers of ten. Power laws y = axⁿ become straight lines on log–log axes with slope n, and exponentials become straight lines on semi-log axes. Decibels and the Richter scale are logarithmic.
A 20 dB increase in sound level means a 100-fold increase in intensity.
Equal distances on a log axis are equal ratios, not equal differences, and zero cannot appear on it.
Frequently asked questions
What are the seven SI base units?
The metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance) and candela (luminous intensity).
What is the difference between accuracy and precision?
Accuracy is how close a measurement is to the true value. Precision is how consistently repeated measurements agree with each other. A measurement can be precise but inaccurate if an instrument has a systematic offset.
How many significant figures should I keep?
Keep no more digits than your least precise input. For example, multiplying 2.5 m by 3.14 gives an answer with two significant figures, because 2.5 has two.
Why does physics need so much maths?
Physics describes how quantities change and relate to each other, and maths is the precise language for that. You do not need advanced maths to start, but you will gradually use algebra, graphs, vectors and then calculus.
How do I know if my answer is reasonable?
Check the units, estimate the order of magnitude and compare with a simple case you already know. A wrong answer often looks wrong in size or units before any arithmetic is checked.
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