Uncertainty & measurement
Gradient Uncertainty Calculator
Enter the steepest and shallowest acceptable gradients from your graph. Supply the best gradient or use their midpoint.
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
Δm = (m_max − m_min)/2
p_m = (Δm/|m_best|) × 100%
| Symbol | Meaning |
|---|---|
| m_max, m_min | Numerically largest and smallest acceptable slopes. Negative slopes retain their signs. |
| m_best | Best-fit gradient, or the midpoint when omitted. |
| Δm | Absolute gradient uncertainty under the half-range convention. |
When to use this calculator
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.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- 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
(2.4 ± 0.2) m/s
Common mistakes
- 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.