Which uncertainty belongs in your calculation?
An absolute uncertainty has the same units as the quantity: 0.730 ± 0.003 m. A fractional uncertainty divides its absolute uncertainty by the measured value: 0.003/0.730 ≈ 0.00411. Percentage uncertainty multiplies that fraction by 100, giving approximately 0.411%.
A percentage error is different: it compares an observed result with a justified reference value. A plausible result can still have weak evidence if its uncertainty was not established from the measuring procedure.
Try the propagation with your own numbers
This is a learning calculator, not a substitute for recording raw data, graphing repeats, or consulting your Physics teacher about your method. It assumes an ideal small-angle simple pendulum and independent measurements for the elementary worst-case estimate.
Period T = t/n: 1.7167 ± 0.0104 s
Fractional length uncertainty: 0.411%.
Fractional uncertainty from T²: 1.214%.
Combined worst-case fractional uncertainty: 1.625%.
Estimated g = 4π²L/T²: 9.779 ± 0.159 m/s² (unrounded, for checking the calculation).
The classroom worst-case uncertainty convention adds fractional terms; it is not a statistical confidence interval. This tool does not model covariance, calibration bias or systematic error. Round the final answer appropriately and justify the measurement uncertainties.
One measurement, traced through six decisions
These figures are deliberately simulated teaching values, not an observed experiment, an official exemplar or a graded sample. What matters is the auditable calculation path.
| Processing step | Value | Reason to inspect |
|---|---|---|
| Read the timer | 24 swings take 41.20 ± 0.25 s | A stopwatch display showing hundredths of a second does not prove reaction-time accuracy. |
| Divide by 24 exact swings | T = 1.7167 ± 0.0104 s | Twenty-four is an exact count; the timing uncertainty divides by 24 too. |
| Square the period | T² = 2.9469 s² with ≈1.214% fractional uncertainty | Squaring doubles the period's fractional uncertainty; do not just square ±0.0104. |
| Use the measured length | L = 0.730 ± 0.003 m | Measure pivot to bob centre, not merely the free string. |
| Derive g = 4π²L / T² | g ≈ 9.779 m/s²; fractional uncertainty ≈1.625% | Combine 0.411% for L with 2 × 0.607% for T by the classroom worst-case propagation convention. |
| Report result at sensible precision | g ≈ 9.8 ± 0.2 m/s² | Do not claim that this single illustrative result proves the model or identifies all systematic errors. |
How does uncertainty change your conclusion?
Start by naming the actual interval. In this example, 9.8 ± 0.2 m/s² is compatible with many nearby values. Compare the estimate only with a suitably justified local reference and the conditions of the pendulum model; do not treat 9.81 m/s² as a universal constant at all places and heights.
Then rank method limits by their causal effect. The 0.25 s timing uncertainty dominates the 0.003 m length uncertainty in this example: their fractional contributions to the derived result are 1.214% and 0.411% respectively. An automated light gate or more reliable timing procedure addresses the dominant term more directly than a more precise ruler. The experiment may also have systematic errors from amplitude, pivot friction, length definition or non-planar swinging; those require separate evidence.
If your report uses a fitted T²-versus-L graph, the gradient and its uncertainty are your key processed data. A one-point calculation is a teaching aid, not a replacement for the graph and evaluation required by your actual investigation.
Four errors to search for before submission
- Calling the stopwatch's smallest displayed digit its total measurement uncertainty while ignoring human start/stop reaction time.
- Dividing the measured time by the number of oscillations without dividing its absolute uncertainty too.
- Using the uncertainty in T unchanged for T² instead of doubling the fractional uncertainty.
- Confusing worst-case addition of relative uncertainties with statistically combined standard uncertainties. Explain which convention applies to your analysis.
Next: inspect the actual scientific investigation
Take your own raw measurement and method to the dedicated Physics IA example. Use the official subject criteria to judge whether the processed evidence really supports your conclusion. The site's AI-assisted feedback is not an official IB grade.
Review my Physics draft →Sources & verification
Primary-source references used to verify key assessment facts on this page. Last source check: October 14, 2026.
The formulas follow the IB Physics course's classroom propagation conventions. The teaching example is original and simulated. For research-grade standard uncertainties, use the applicable statistical measurement model and the NIST uncertainty guidance.
- IB Physics guide, first assessment 2025Primary authority for the current scientific investigation criteria and the treatment of uncertainties, measurement, graphs and data analysis.
- NIST: Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement ResultsReference for standard uncertainty, independence, and uncertainty combination; distinguishes statistically combined uncertainty from the simplified examination conventions.
- IB Physics examples and current assessment contextExisting iBacalao worked pendulum investigation and four science IA criteria; not an official marked student exemplar.