Uncertainty & measurement
Gradient uncertainty
Estimate uncertainty from maximum and minimum gradients.
Your measurements
Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
Calculated locally. No account or uploads.
Result & working
ExampleThe calculator is loading. You can read the worked example below.
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Interpretation & assumptions
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Numerically largest and smallest acceptable slopes. Negative slopes retain their signs. | |
| Best-fit gradient, or the midpoint when omitted. | |
| Absolute gradient uncertainty under the half-range convention. |
Worked example
- Maximum acceptable gradient
- 2.6
- Minimum acceptable gradient
- 2.2
- Best gradient (optional)
- 2.4
- Result unit (optional)
- m/s
- Uncertainty significant figures
- 1 significant figure
(2.4 ± 0.2) m/s
Follow the example steps
- Δm = (m_max − m_min) / 2 = (2.6 − (2.2)) / 2 = 0.2
- Best gradient supplied: 2.4
- Percentage uncertainty = Δm / |m_best| × 100 = 0.2 / |2.4| × 100 = 8.333333%
- Rounded result: (2.4 ± 0.2) m/s
Common mistakes
Use the absolute best gradient in percentage uncertainty.
Incorrect approach
m_best = −2, Δm = 0.2: 100 × 0.2/(−2) = −10%
Correct approach
100 × 0.2/|−2| = 10%
More checks before you submit
- Do not swap steepest by appearance with numerically maximum when slopes are negative.
- Use |m_best| so the percentage uncertainty stays non-negative.
- Zero best gradient makes percentage uncertainty undefined.
Method notes
Draw the maximum and minimum gradients consistent with your error bars according to your lab instructions. Calculate each using widely separated points on the line, not necessarily measured data points, then enter the slopes here.
This calculator cannot decide whether a line is acceptable from slopes alone. Half the slope range is a common school-lab convention. If your best gradient is off-center, ± half the range does not give the exact interval endpoints; retain the asymmetric bounds when appropriate.