Raw numbers on their own don’t answer anything. Processing is where you turn them into something meaningful — averaging your repeats, carrying uncertainties through every calculation, and reshaping the data so a graph reveals the relationship you’re after. This is the calculation phase, and doing it cleanly (with one worked example shown in full) is where a lot of IA marks are won or lost.
📘 What you need to know
Show one full worked example for every type of calculation you do
Average your repeat trials — and exclude anomalies before you do
Add/subtract → add the absolute uncertainties; multiply/divide → add the percentage uncertainties
For a quantity raised to a power, multiply the percentage uncertainty by that power
Your answer’s significant figures match the least precise raw data used
Linearise curved relationships so a straight-line graph does the heavy lifting
Averaging and showing your working
When you have repeat trials, the first step is a mean value — that’s what feeds every later calculation. Crucially, exclude any anomalies first: an outlier you flagged during collection shouldn’t be dragged into the average, or it pollutes everything downstream.
The golden rule of the whole phase: show one full worked example for each kind of calculation. Even if a spreadsheet crunched all fifty rows, the assessor needs to see, once, exactly how you got from raw numbers to a processed value. That single visible calculation is what earns the marks.
Propagating uncertainties
Every raw measurement carries an uncertainty, and those must be carried through your calculations to the final result. The rule you use depends on the operation.
Adding or subtracting
add the absolute uncertainties
If you find a length from L = final position − initial position, and each position is read on a ruler to ±0.5 mm, then the uncertainty in L is 0.5 + 0.5 = 1 mm.
Multiplying or dividing
add the percentage (or fractional) uncertainties
To find a resistance from R = V ÷ I, the percentage uncertainty in R is (% uncertainty in V) + (% uncertainty in I).
Raising to a power
multiply the percentage uncertainty by the power
For kinetic energy Ek = ½mv2, the percentage uncertainty is (% in m) + 2 × (% in v) — the square doubles the contribution from v.
+ or −
→ add →
absolute unc.
× or ÷
→ add →
% unc.
power n
→ ×n →
% unc.
Quick recap: quote your final absolute uncertainty to one significant figure, then round the value to match its decimal place (e.g. T = 1.37 ± 0.01 s).
Significant figures
Your processed answer should carry the same number of significant figures as the least precise piece of raw data that went into it. Writing down the full calculator display (1.36666… s) is a classic error — it claims a precision your measurements never had.
WE 1
A pendulum of length 0.450 m is timed for 20 oscillations, three times: 27.3 s, 27.5 s, 27.2 s. The stopwatch reads to ±0.2 s. Find the period and its uncertainty.
Step 1 — average time for 20 swingst₀ = (27.3 + 27.5 + 27.2) ÷ 3 = 27.33 sStep 2 — period of one swing (divide by 20)T = 27.33 ÷ 20 = 1.3666 sT = 1.37 s (3 s.f.)Step 3 — propagate the uncertainty
% uncertainty in t₀ = (0.2 ÷ 27.33) × 100 = 0.73%
20 is exact, so T carries the same 0.73%.
absolute unc. = (0.73 ÷ 100) × 1.3666
= 0.010 s (to 1 s.f.)T = 1.37 ± 0.01 s
WE 2
A single length of resistance wire gives V = 3.15 ± 0.01 V and I = 1.42 ± 0.01 A. Calculate the resistance and its uncertainty.
Step 1 — calculate R = V ÷ IR = 3.15 ÷ 1.42 = 2.218 ΩV and I both have 3 s.f., so R does too → 2.22 ΩStep 2 — percentage uncertainties
% in V = (0.01 ÷ 3.15) × 100 = 0.32%
% in I = (0.01 ÷ 1.42) × 100 = 0.70%
Step 3 — division, so add the percentages% in R = 0.32 + 0.70 = 1.02%
absolute unc. = (1.02 ÷ 100) × 2.218 = 0.02 Ω (1 s.f.)
R = 2.22 ± 0.02 Ω
Presenting processed data
Processed values go in a neat, numbered table — and it’s good practice to show raw and processed data side by side in one table. Each column header carries the quantity, its unit, and the absolute uncertainty; the independent variable sits in the first column. Keep decimal places consistent and matched to your quoted uncertainties.
🎨 A well-formed scientific graph has
A descriptive title — name both variables, e.g. “period squared against pendulum length”.
Labelled axes with units — independent variable on the x-axis, dependent on the y-axis.
A sensible scale — points should fill at least half the grid; justify any axis that doesn’t start at zero.
Clear points, error bars, and a line of best fit — the line runs through the trend, not dot-to-dot.
Linearisation
Many physics relationships aren’t straight lines — and a curve is hard to read a precise relationship from. So we linearise: rearrange the known equation until plotting the data gives a straight line. A straight line is easy to test, and its gradient often hands you a physical quantity directly.
Take the pendulum, whose period follows T = 2π√(L ÷ g). Squaring both sides rearranges it into straight-line form:
Linearised pendulum equationT2 = (4π2 ÷ g) × L
Compare that with y = mx + c: if you plot T2 on the y-axis against L on the x-axis, you get a straight line through the origin with gradient 4π2 ÷ g. Measure that gradient and you can solve for g.
Plotting T2 against L straightens the curve — a line through the origin confirms direct proportionality, and its gradient gives g.
💡 Top tips
Show one full worked example — even with a spreadsheet, walk the assessor through one set of values from raw to processed.
Match the operation to the rule — add absolutes for ±, add percentages for ×/÷, multiply by the power for xn.
Round the uncertainty to 1 s.f. first, then quote the value to the same decimal place — not the full calculator display.
Independent variable always on the x-axis — and when you linearise, plot the rearranged quantities, not the raw ones.
⚠ Common mistakes
Including anomalies in the average instead of excluding them first
Adding absolute uncertainties for a multiplication or division (should be percentages)
Quoting the full calculator display — more significant figures than the raw data justifies
Forgetting to double the percentage uncertainty for a squared quantity like v2
Up next: Interpreting Results — reading the story in your graph. Describing and explaining the trend, using the gradient and intercept, spotting anomalies, and using the language of accuracy, precision, reliability, and validity properly.
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