📐 Percent Error Calculator

Analyze errors between experimental measurements and true values. Calculate absolute, relative, and percent errors for up to 10 measurements with visualization.

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Types of Measurement Errors: Absolute, Relative, and Percent Error

Error analysis is essential in scientific experiments and engineering measurements. Absolute Error represents the difference between measured and true (theoretical or standard) values, calculated as EA = |Measured - True|. For example, if measuring an object with true value 100g yields 98g, the absolute error is |98 - 100| = 2g. Absolute error has the same units as the measurement. Relative Error is absolute error divided by true value: ER = |Measured - True| / |True|, giving 0.02 in this example. Percent Error is relative error multiplied by 100%: E% = 0.02 × 100% = 2%.

Multiple Measurements and Mean Absolute Error (MAE)

Measuring the same object multiple times yields different values due to random error. If measuring liquid with true value 50.0mL five times gives 49.8, 50.2, 49.9, 50.3, 50.1mL, absolute errors are 0.2, 0.2, 0.1, 0.3, 0.1mL. Mean Absolute Error (MAE) is the average of all absolute errors: MAE = (0.2 + 0.2 + 0.1 + 0.3 + 0.1) / 5 = 0.18mL. MAE evaluates overall measurement system accuracy.

Error Propagation: How Errors Transfer in Calculations

Addition/Subtraction Rule: For z = x ± y, absolute error δz = √(δx² + δy²). If x = 10.0 ± 0.2cm and y = 5.0 ± 0.1cm, then z = 15.0cm with δz = √(0.2² + 0.1²) ≈ 0.22cm. Multiplication/Division Rule: For z = x × y or z = x / y, relative error δz/|z| = √[(δx/|x|)² + (δy/|y|)²]. Power Rule: For z = xⁿ, δz/|z| = |n| × (δx/|x|). Powers amplify errors significantly.

Significant Figures: Representing Precision

Significant figures indicate measurement precision. Rules: ① All non-zero digits are significant (123 → 3). ② Zeros between non-zero digits are significant (1002 → 4). ③ Trailing zeros after decimal are significant (1.20 → 3, but 1.2 → 2). ④ Integer trailing zeros are ambiguous (1200 could be 2 or 4). Use scientific notation for clarity. Addition/subtraction matches fewest decimal places; multiplication/division matches fewest significant figures.

Systematic vs Random Errors: Understanding the Difference

Errors are classified as Systematic Error or Random Error. Systematic errors consistently bias measurements in one direction (e.g., scale always reads +2g high). They affect accuracy and require calibration to fix. Random errors scatter measurements unpredictably around the true value. They affect precision and decrease with more measurements. Ideal measurements are both accurate (no systematic error) and precise (small random error).

Frequently asked questions

Can percent error be negative?

This calculator uses absolute values, so percent error is always 0 or greater. Whether the measured value is higher or lower than the true value, it is computed as |Measured - True|.

What happens if I set the true value to 0?

Relative and percent errors divide by the true value, so they are undefined when the true value is 0 (division by zero). In that case only the absolute error is meaningful.