Uncertainty & measurement
Agreement Within Uncertainty Calculator
Ask whether the stated intervals overlap. Use zero reference uncertainty only when the reference is treated as exact.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
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Result & working
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Step-by-step working
The formula
A = [a − Δa, a + Δa]; B = [b − Δb, b + Δb]
Intervals overlap when |a − b| ≤ Δa + Δb
| Symbol | Meaning |
|---|---|
| a, b | Values in the same unit. |
| Δa, Δb | Non-negative interval half-widths with an explained meaning. |
When to use this calculator
Use interval overlap as a simple school-lab consistency check. A touching endpoint counts as overlap. A result can have a small percentage error yet fail this check if its claimed uncertainty is very small.
Overlap means the measurements can share a value within these stated bounds. It does not prove equality or validate the apparatus. Non-overlap suggests investigating the model and uncertainty estimates.
This is not a hypothesis test, p-value or confidence-level calculation. Standard-deviation bars need a statistical interpretation before using them as interval bounds.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- A = 9.7 ± 0.2 m/s²; B = 9.81 ± 0 m/s².
- Separation = |9.7 − (9.81)| = 0.11 m/s².
- Sum of interval half-widths = 0.2 + 0 = 0.2 m/s².
- 0.11 ≤ 0.2: The stated intervals overlap.
The stated intervals overlap.
Common mistakes
- Do not claim that overlap proves the theory.
- Compare quantities in matching units.
- Keep systematic effects in view even when the random spread is small.