20 min read

Error Propagation in Calculations

When measurements with known percentage errors are combined, their percentage errors combine in predictable ways.

How Percentage Errors Combine

Quick rules for percentage error
Quick rules for percentage error

These are quick, approximate rules — the exact bounds method from the last two lessons is more precise, but these rules are fast for estimating.

Example 1 — squaring a measurement

A square's side is measured with a 2% error. Area = side². Estimate the percentage error in the area. 1 Squaring means the power is n = 2 2 Multiply the percentage error by n : 2% \times 2 Answer: \approx 4%

Example 2 — multiplying two different measurements

A rectangle's length has a 3% error and its width has a 2% error. Estimate the percentage error in its area (length \times width). 1 Multiplying two independent measurements: add their percentage errors 2 3% + 2% Answer: \approx 5%

Practice

A cube's edge length has a 1.5% error. Estimate the percentage error in its volume (edge³).

Your answer

How Percentage Errors Combine

Quick rules for percentage error
Quick rules for percentage error

These are quick, approximate rules — the exact bounds method from the last two lessons is more precise, but these rules are fast for estimating.

Example 1 — squaring a measurement

A square's side is measured with a 2% error. Area = side². Estimate the percentage error in the area. 1 Squaring means the power is n = 2 2 Multiply the percentage error by n : 2% \times 2 Answer: \approx 4%

Example 2 — multiplying two different measurements

A rectangle's length has a 3% error and its width has a 2% error. Estimate the percentage error in its area (length \times width). 1 Multiplying two independent measurements: add their percentage errors 2 3% + 2% Answer: \approx 5%

Practice

A cube's edge length has a 1.5% error. Estimate the percentage error in its volume (edge³).

Your answer