IB Physics Error Bars & Uncertainty Propagation: Complete FAQ

Identify whether the question wants absolute or percentage uncertainty, then apply the matching rule — add absolute uncertainties for addition/subtraction, add percentage uncertainties for multiplication/division. State your final answer with sensible significant figures and matching uncertainty, and show your working, since examiners award marks for method as much as the final number.

Error bars are short lines drawn through a data point showing the range within which the true value probably sits. In IB Physics they represent the absolute uncertainty of that measurement, and the IB expects you to draw them consistently on any graph in Paper 3 and your Internal Assessment.

Percentage uncertainty equals the absolute uncertainty divided by the measured value, multiplied by 100. A length of 12.0 cm measured to ±0.1 cm gives (0.1 ÷ 12.0) × 100 = 0.83%. Quote your answer to two significant figures unless the mark scheme specifies otherwise.

When adding or subtracting measurements, add the absolute uncertainties together — never the percentages. If a = 5.0 ± 0.2 cm and b = 3.0 ± 0.1 cm, then a + b = 8.0 ± 0.3 cm. The same rule applies whether the quantities are being added or subtracted.

For multiplication or division, convert each uncertainty to a percentage first, then add the percentages together. If a = 5.0 cm ± 2% and b = 3.0 cm ± 3%, then a × b = 15 cm² ± 5%. Convert back to an absolute value only at the very end.

Draw a best-fit line through your data, then draw the steepest and shallowest lines that still pass through every error bar. Calculate each gradient — the uncertainty in the gradient is half the difference: Δm = (m_max − m_min) ÷ 2.

Uncertainty skills appear across all three IB Physics papers but are assessed most heavily in Paper 3's data-based question and in the Internal Assessment. According to the IB Physics guide (first exams 2025), uncertainty and error analysis sit under the 'Tools' skills that underpin every assessment component, not just one paper.

Common command terms include 'calculate' for numerical uncertainty values, 'determine' for finding a gradient or its uncertainty from given data, 'sketch'/'draw' for error bars and best/worst-fit lines, and 'estimate' for a reasonable uncertainty based on equipment precision. Each term signals exactly how much working the examiner expects.

In Paper 3, uncertainty and graph-based questions typically carry three to six marks within a longer data-analysis question, split between calculating a value, stating its uncertainty, and reading or drawing error bars correctly. In the IA, uncertainty treatment sits within the 'Analysis' criterion, worth 6 of the 24 total marks.

The biggest mistake I see is students adding percentage uncertainties when the calculation actually calls for absolute uncertainties, or the reverse — mixing up the addition/subtraction rule with the multiplication/division rule. The second most frequent slip is quoting a value and its uncertainty to mismatched significant figures.

Draw a single smooth line or curve that passes as close as possible to the centre of every error bar, not necessarily through each point exactly. Then draw the steepest and shallowest lines that still touch every bar's range — these give the maximum and minimum gradients for your uncertainty calculation.

Uncertainty propagation isn't conceptually difficult — most students grasp the four core rules within a lesson or two. What actually costs marks is careless arithmetic or mixing up the addition and multiplication rules under time pressure, particularly in the extended data question on Paper 3.

Full marks come from consistency: state the uncertainty of every raw measurement, propagate it correctly through every calculation, and show error bars with best-fit and worst-fit lines on any graph. The IA's 'Analysis' criterion rewards a clear, consistent uncertainty trail more than perfect precision in any single number.

Uncertainty analysis sits inside the 'Analysis' criterion of the IB Physics Internal Assessment, worth 6 of the 24 total marks — a quarter of the whole grade. Students who treat uncertainty as an afterthought, added at the very end, consistently lose marks here even when their raw data and conclusion are strong.

Repeated practice with real datasets builds this skill fastest — working through past Paper 3 questions, redoing IA-style calculations, and checking answers against a mark scheme. On RevisionPrep, Topical Worksheets and Mock Papers give students graded practice on uncertainty propagation with full worked solutions, so they can see exactly where marks are gained or lost.