Experimental data & uncertainty · SL/HL
Uncertainty Propagation Calculator
For sums and differences, absolute uncertainties add. For products and quotients, percentage uncertainties add. Raising to a power is an HL-only chemistry skill in the current guide.
Your values
Start with the example or enter your own values. Use a dot for decimals and e for scientific notation.
Calculated locally. No account or input upload.
Result & working
ExampleThe calculator is loading. The worked example is also shown below.
Step-by-step working
The formula
z = a ± b: Δz = Δa + Δb
z = ab or a/b: percentage uncertainties add
z = aⁿ (HL): percentage uncertainty ≈ |n| × percentage uncertainty in a
| Symbol | Meaning |
|---|---|
| a,b | Measured quantities. |
| Δa,Δb | Absolute uncertainties. |
When to use this calculator
These are the linear propagation rules specified for course data processing. They are not a replacement for a full statistical uncertainty model.
Worked example
The page opens with these example values. The result below is pre-generated for reference.
- z = 25 ÷ 24.6 = 1.01626
- pₐ = 0.2%; pᵦ = 0.203252%
- p_z ≈ pₐ + pᵦ = 0.403252%
- Δz ≈ |z|p_z/100 = 0.00409809
- Rounded result: (1.016 ± 0.004)
(1.016 ± 0.004)
Common mistakes
- Absolute uncertainties add even when measured values are subtracted.
- Power propagation is HL-only in the current Chemistry guide.