Percent Error Calculator

Math

Calculate the percentage error, absolute error, and relative error between an experimental measured value and the theoretical accepted value.

Percent Error

2.0408%

▼ Underestimation (Difference: -0.2000)

Absolute Error 0.2000

Relative Error 0.020408

Step-by-Step Calculation

1. Calculate Absolute Error

|V_E - V_T| = |9.6 - 9.8| = |-0.2000| = 0.2000

Find the absolute difference between the experimental (measured) value and the theoretical (accepted) value.

2. Divide by Theoretical Value

|V_E - V_T| / |V_T| = 0.2000 / |9.8| = 0.020408

Divide the absolute error by the true value to determine the relative error ratio.

3. Convert to Percentage

0.020408 × 100% = 2.0408%

Multiply by 100 to express the discrepancy as a percentage error.

How This Calculator Works

Percent error is a critical quantitative metric in experimental sciences, physics, chemistry, and quality control engineering. It quantifies how far an empirical experimental observation deviates from the accepted, standard, or theoretical true value.

📐 Percent Error & Relative Error Formulas

V_exp: Experimental or measured value obtained in testing

V_theo: Accepted theoretical, true, or standard literature reference value

Absolute Error: Magnitude of deviation in identical measurement units

Relative Error: Dimensionless ratio of absolute error divided by theoretical value

Key Mathematical Rules & Properties

Absolute Value Convention

Percent error is conventionally written as a non-negative percentage using absolute values, although the direction of error indicates overestimation or underestimation.

Theoretical Non-Zero Requirement

The theoretical reference value must not be zero (V_theo ≠ 0), because division by zero is mathematically undefined.

Precision vs Accuracy

High precision means repeated measurements are close to each other. High accuracy means the measurements are close to the theoretical value (low percent error).

Acceptable Error Tolerances

Introductory student laboratories often tolerate 1% to 5% error. Industrial manufacturing often requires error margins below 0.1% or 6-Sigma tolerances.

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Worked Example: Measuring Acceleration Due to Gravity

A student pendulum experiment measures gravity as 9.62 m/s² against the standard Earth constant of 9.81 m/s².

Identify values: Experimental V_exp = 9.62 m/s², Theoretical V_theo = 9.81 m/s².
Calculate absolute error: |9.62 - 9.81| = |-0.19| = 0.19 m/s².
Calculate relative error: 0.19 / 9.81 ≈ 0.019368.
Multiply by 100%: 0.019368 × 100% ≈ 1.94%.
Direction: Underestimation by 0.19 m/s² (observed value was smaller).

Final Answer: 1.94% (Underestimation by -0.19 m/s²)

Frequently Asked Questions

Can percent error be negative?

Most scientific standards use the absolute value formulation (|V_exp - V_theo| / |V_theo|) × 100%, making percent error strictly positive. However, some instructors allow signed percent error without the absolute value to explicitly denote underestimation (-) or overestimation (+).

What should you do if theoretical value is zero?

If theoretical value is zero, percent error cannot be calculated. In such cases, scientists report absolute error instead.

What causes experimental error?

Errors arise from systematic errors (instrument calibration issues, zero-point offset) and random errors (human reaction times, environmental temperature fluctuations, electrical noise).

How does percent error differ from percent difference?

Percent error is used when one value is definitively known to be the "true" or theoretical reference. Percent difference is used when comparing two experimental values when neither is known to be the true standard.

Understanding your calculation

Method, example and limitations

How the calculation works

Percent error compares a measured value with a reference: absolute difference divided by the absolute reference value, multiplied by 100.

Example to check

A measured value of 98 and a reference of 100 differ by 2, giving an absolute percent error of 2%.

Before using the result

A zero reference makes relative percent error undefined. Distinguish signed error, absolute percent error and percentage difference between two peer values.

Calculation methodology · Report a result that needs review