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Uncertainties in IB Physics: Absolute, Percentage and Propagation
4 min readBy Renzo DiazLast reviewed October 7, 2026
In IB Physics an uncertainty is written three ways: absolute (the ± in the quantity's own units), fractional (the absolute uncertainty divided by the value) and percentage (the fractional uncertainty times 100). The data booklet for the current course gives three propagation rules: for a sum or difference, add the absolute uncertainties; for a product or quotient, add the fractional uncertainties; for a power, multiply the fractional uncertainty by the power. The same skills earn marks in Paper 1B and in the internal assessment.
It is easy to treat uncertainties as decoration: a ± added at the end, because the mark scheme seems to want one. They are the opposite. An uncertainty says how far a result can be trusted, and the current course asks for it everywhere data appears: in the internal assessment, in Paper 1B, and in Paper 2 whenever a question gives measured values.
This article sets out what the IB Physics guide (first assessment 2025) asks for, the three rules in the data booklet, and two worked examples, then separates what the guide fixes from the conventions it leaves to the student.
An uncertainty is not decoration added at the end. It is the statement of how far the result can be trusted.
Key takeaways
- Three forms: absolute Δx, fractional Δx/x, percentage 100 × Δx/x.
- Sums and differences: the absolute uncertainties add, even when you subtract.
- Products, quotients and powers: the fractional uncertainties add, and a power n multiplies its fractional uncertainty by n.
- Graphs: uncertainty bars, maximum and minimum gradient lines, and the uncertainty of a gradient and an intercept are all in the 2025 guide.
- Where it scores: the internal assessment's data analysis criterion, and Paper 1B, where 79 of the 100 marks in the 2025 papers were for data skills.
What the 2025 IB Physics guide asks for
The guide lists uncertainties among the mathematical and experimental skills every Physics student is expected to use, at SL and HL alike. They are not a topic of their own; they run through the whole course. The table puts each skill in plain terms.
| Skill in the guide | In practice |
|---|---|
| Recording each measurement with its uncertainty as a ± range | Every measured value in a table carries its ± and its unit |
| Writing uncertainties in absolute, fractional or percentage form, sensibly rounded | Use the form the calculation needs |
| Carrying uncertainties through sums, differences, products, quotients and powers | The three data booklet rules in the next sections |
| Working out percentage error and percentage uncertainty | Compare a result with an accepted value, and with its own uncertainty |
| Drawing and reading uncertainty bars | Error bars on the points of a graph |
| Drawing the steepest and shallowest lines, and finding the uncertainty of a gradient and an intercept | The uncertainty of a quantity read from a straight-line graph |
| Discussing how uncertainties, and random or systematic errors, affect a conclusion | The evaluation of an investigation |
Source: IB Physics guide (first assessment 2025), "Skills in the study of physics", pp. 29–30, and the inquiry-process skills. Paraphrased; checked 7 October 2026.
Absolute, fractional and percentage uncertainty
The absolute uncertainty is the ± written in the quantity's own units: a length of 0.600 ± 0.002 m has an absolute uncertainty of 0.002 m. The fractional uncertainty divides it by the value, 0.002 / 0.600 ≈ 0.0033, and has no unit. The percentage uncertainty is the fractional one times 100, here about 0.33%.
The three forms say the same thing in different ways, and each has its use: absolute for writing a result, fractional and percentage for comparing the precision of different measurements and for propagating through products and powers.
| Quantity | Value | Absolute | Fractional | Percentage |
|---|---|---|---|---|
| Pendulum length L | 0.600 m | ± 0.002 m | 0.0033 | 0.33% |
| Period T | 1.56 s | ± 0.02 s | 0.013 | 1.3% |
Illustrative values chosen for this article; the arithmetic is exact.
Worked example
Timing ten swings, then dividing
Ten oscillations take 15.6 ± 0.2 s. One period is 15.6 / 10 = 1.56 s, and dividing by the exact number 10 divides the absolute uncertainty too: ± 0.02 s. The percentage uncertainty is unchanged at 1.3%. Timing many swings is how a hand-held stopwatch gives a precise period.
The three propagation rules
The data booklet gives three rules, and between them they cover every calculation the guide expects. Numbers that are exact, such as a count of oscillations or the 4π² in a formula, carry no uncertainty.
| The result is… | Rule | Example |
|---|---|---|
| A sum or a difference, y = a ± b | Add the absolute uncertainties: Δy = Δa + Δb | 25.4 ± 0.1 cm minus 24.9 ± 0.1 cm is 0.5 ± 0.2 cm |
| A product or a quotient, y = ab / c | Add the fractional uncertainties: Δy/y = Δa/a + Δb/b + Δc/c | Speed from 2.0% on distance and 1.5% on time: 3.5% |
| A power, y = aⁿ | Multiply the fractional uncertainty by the power: Δy/y = n × Δa/a | Area of a square from a 1.0% side: 2.0% |
Source: Physics data booklet (first assessment 2025), "Uncertainties", p. 3. Examples are illustrative. Checked 7 October 2026.
Watch the subtraction
Two good measurements, one poor difference
Each length in the first row is known to under 0.5%. Their difference, 0.5 ± 0.2 cm, is uncertain by 40%. Subtracting close values keeps the absolute uncertainties and loses the value, which is why a method that relies on a small difference is a weak one.
Worked example
g from a pendulum
With g = 4π²L / T², the fractional uncertainties add, and T counts twice because it is squared: 0.33% + 2 × 1.28% ≈ 2.9%. The value is g = 4π² × 0.600 / 1.56² ≈ 9.73 m s⁻², so the absolute uncertainty is about 0.28 m s⁻². Rounded, the result is g = 9.7 ± 0.3 m s⁻².
Percentage error is not percentage uncertainty
The guide asks for both, and they answer different questions. The percentage uncertainty says how precise a result is: in the pendulum example, 2.9%. The percentage error compares the result with an accepted value: against the data booklet's 9.8 m s⁻², the result 9.73 m s⁻² is out by about 0.7%.
Read together, they make an evaluation. Here the error is smaller than the uncertainty, so the result agrees with the accepted value within its own uncertainty. When the error is much larger than the uncertainty, something in the method is shifting every reading the same way. The guide's own distinction applies: random errors make results imprecise, and repeating measurements reduces their effect; systematic errors make results inaccurate, and repeating does not remove them.
Uncertainty bars and the uncertainty of a gradient
Many investigations end with a straight-line graph whose gradient or intercept is the answer. The guide expects its uncertainty to come from the graph itself.
From uncertainty bars to the uncertainty of a gradient
Plot each point with its uncertainty bars
A bar shows the ± of the plotted quantity, on whichever axes it is not negligible.
Draw the line of best fit
Its gradient, with its unit, is the result.
Draw the steepest and the shallowest lines
Both must pass through all the uncertainty bars. The guide asks for them by eye, with reasonable accuracy; no statistical fit is required.
Turn the spread into an uncertainty
A common convention is half the difference between the maximum and minimum gradients. The intercept is treated the same way, from where the two lines cross the axis.
Write the result and interpret it
Gradient ± uncertainty, with units, then what it means for the quantity you set out to find.
What the guide leaves to you
The guide asks for uncertainties rounded to a sensible number of significant figures and level of precision, and does not fix how a reading's uncertainty is estimated. Schools use a few widely shared conventions; none is an IB rule, so an investigation should say which one it used and why.
| Situation | Common convention |
|---|---|
| Reading an analogue scale | Half the smallest division, or more if the reading is harder than the scale suggests |
| Reading a digital display | One unit in the last digit shown |
| Repeated readings of the same quantity | Half the range of the readings, about their mean |
| Rounding an uncertainty | One significant figure, or two when the first is a 1 |
| Rounding the value | To the same decimal place as its uncertainty |
Conventions, not IB requirements: the IB Physics guide (first assessment 2025) asks only for an appropriate number of significant figures and level of precision.
Where uncertainties earn marks
In the internal assessment, the scientific investigation is marked on four criteria of 6 marks each: research design, data analysis, conclusion and evaluation. The data analysis criterion rises through its bands partly on how the uncertainties are handled: little sign that they were considered at the bottom, uncertainties handled properly throughout at the top. A fully consistent conclusion is one that interprets the processed data together with its uncertainties, and the evaluation turns on the errors and weaknesses behind them. Each of the 15 IB Physics IA ideas names the uncertainty that will dominate it.
In the written exams, Paper 1B is built on data. In the five 2025 sittings, 79 of its 100 marks were for data skills: graphs, gradients, uncertainties and method. The count of the 2025 Physics exams shows how those marks were spread.
Terms used in this article
- Absolute uncertainty
- The ± attached to a value, in the value's own units.
- Fractional uncertainty
- The absolute uncertainty divided by the value; also called the relative uncertainty. It has no unit.
- Percentage uncertainty
- The fractional uncertainty multiplied by 100.
- Percentage error
- How far a result is from an accepted value, as a percentage of the accepted value.
- Random and systematic errors
- Random errors scatter readings and make results imprecise; repeating measurements reduces their effect. Systematic errors shift every reading the same way and make results inaccurate; repeating does not remove them.
- Uncertainty bar
- A bar drawn through a plotted point to show the ± of that point; also called an error bar.
Questions about uncertainties in IB Physics
How do you calculate percentage uncertainty?
Divide the absolute uncertainty by the measured value and multiply by 100. A length of 0.600 ± 0.002 m has a percentage uncertainty of about 0.33%.
Do uncertainties add when you subtract two values?
Yes: for a sum or a difference, the absolute uncertainties add. Subtracting close values can therefore leave a large percentage uncertainty, as 25.4 ± 0.1 cm minus 24.9 ± 0.1 cm = 0.5 ± 0.2 cm shows.
How do uncertainties propagate through multiplication, division and powers?
Add the fractional uncertainties, and multiply a power's fractional uncertainty by the power. These are the rules printed in the IB Physics data booklet.
How do you find the uncertainty of a gradient in IB Physics?
From the steepest and shallowest lines that pass through all the uncertainty bars. A common convention takes half the difference between their gradients; the intercept is treated the same way.
Is percentage error the same as percentage uncertainty?
No. Percentage uncertainty measures how precise a result is; percentage error measures how far it is from an accepted value. A result agrees with the accepted value when the error is within the uncertainty.
How many significant figures should an uncertainty have?
The IB guide asks for an appropriate number. A common convention is one significant figure, or two when the first is a 1, with the value rounded to the same decimal place.
Written by
Teaching IB since 2016. Seven years of IB reviews you can check on Google — and named results with the documents behind them.
Last reviewed October 7, 2026
Sources
What the course requires comes from the IB Physics guide (first assessment 2025), and the three propagation rules from the Physics data booklet for the same course, both made available to schools by the IB and paraphrased here. The worked examples use illustrative values chosen for this article. The share of data-skill marks in Paper 1B comes from my own count of the 2025 papers, set out in the linked article. Checked on 7 October 2026.