Uncertainty & measurement
Repeated Measurement Uncertainty & Timing Calculator
Process repeated readings or repeated timings of several oscillations. Keep the school-lab half-range convention separate from statistical standard error.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
Calculated locally. No account or uploads.
Result & working
ExampleThe calculator is loading. You can read the worked example below.
Step-by-step working
The formula
x̄ = Σxᵢ/n; range = x_max − x_min
Δx = max(range/2, supplied uncertainty floor)
T = x̄/N; ΔT = Δx/N; p = 100ΔT/|T|
| Symbol | Meaning |
|---|---|
| n | Number of repeated readings. |
| N | Exact cycle/item count per reading, a positive integer. |
| Floor | An explicitly supplied lower bound for uncertainty. It is not estimated from the data. |
When to use this calculator
Use half the range when that is the convention requested in a school experiment. This tool applies the larger of half-range and the supplied floor; this is a stated reporting convention, not an IB rule for every instrument or a universal statistical formula.
Timing several cycles can reduce the relative effect of a fixed start/stop uncertainty. Count complete oscillations and keep the cycle count exact. The tool also displays sample SD and SEM for comparison, without substituting them for the half-range.
Identical repeated readings do not prove zero uncertainty. Resolution, calibration and method limits still matter. A systematic offset is not removed by repetition.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- Mean = 80.6 / 4 = 20.15 s.
- Range = 20.3 − 20 = 0.3; half-range = 0.15 s.
- Chosen uncertainty = max(0.15, 0.1) = 0.15 s.
- Value per cycle/item = 20.15/10 = 2.015; uncertainty = 0.15/10 = 0.015 s.
- Final reported value: (2.01 ± 0.02) s.
(2.01 ± 0.02) s
Common mistakes
- Do not divide the half-range by √n; that produces neither the half-range nor sample SEM.
- Distinguish repeats n from cycles per timing N.
- Do not remove an extreme value without investigating and explaining it.