Percent Error Calculator

How to Use the Percent Error Calculator

This percent error calculator compares your experimental and theoretical values — enter your experimental value (the result you measured or obtained) and the theoretical value (the accepted, expected, or true value). The calculator instantly returns four results: the absolute percent error, signed percent error, absolute error, and relative error. All outputs update in real time as you type. Use the Share button to copy a URL with your inputs pre-filled.

This tool is designed for students, scientists, and engineers who need to quickly assess the accuracy of a measurement or calculation. For comparing a set of values statistically, see our standard deviation calculator.

The Percent Error Formula

Percent error measures how far your experimental result deviates from the accepted value, expressed as a percentage of the accepted value:

% Error = |Experimental − Theoretical| / |Theoretical| × 100

The absolute value signs ensure the result is always non-negative. If you need to know which direction the error goes — whether your measurement was too high or too low — use the signed percent error: (Experimental − Theoretical) / |Theoretical| × 100.

Step-by-Step Example

A student measures the boiling point of water and gets 98.9°C. The accepted value is 100.0°C.

1. Absolute error: |98.9 − 100.0| = 1.1°C
2. Relative error: 1.1 / 100.0 = 0.011
3. Percent error: 0.011 × 100 = 1.10%
4. Signed percent error: (98.9 − 100.0) / 100.0 × 100 = −1.10% (measured too low)

What If the Theoretical Value Is Zero?

The percent error formula requires dividing by the theoretical value, so it is undefined when the theoretical value is exactly zero. In that case, consider using the absolute error alone, or reformulate the problem with a non-zero reference value.

Absolute Error vs. Relative Error vs. Percent Error

These three related measures each tell you something slightly different about measurement accuracy:

• Absolute error — the raw difference between experimental and theoretical values, in the original units (e.g., 2.5 mL, 0.3 kg). Useful for understanding the size of the error in real-world terms.
• Relative error — absolute error divided by the theoretical value, giving a dimensionless ratio (e.g., 0.025). Useful for comparing accuracy across experiments with different scales.
• Percent error — relative error multiplied by 100 (e.g., 2.50%). The most intuitive form for reporting and comparing results.

When comparing two experiments — say, a mass measurement with 0.5 g error versus a volume measurement with 0.5 mL error — the absolute errors look identical but the relative errors differ if the theoretical values differ. Relative and percent error normalize for scale, making them better for comparison. For percentage-based comparisons between two changing values, our percent decrease calculator may be more appropriate.

What Is a Good Percent Error?

Acceptable percent error depends heavily on the field and application:

• High-school science labs: errors below 5% are generally acceptable; below 2% is excellent.
• Undergraduate chemistry/physics: errors below 3–5% are typical; below 1% indicates very careful technique.
• Pharmaceutical manufacturing: regulatory standards often require less than 1–2% deviation.
• Precision machining: tolerances of ±0.1% or tighter are common for critical components.
• Construction and civil engineering: ±1–5% is typical, depending on the measurement type.

A large percent error does not always mean your experiment failed — it may indicate a need for better equipment, a revised procedure, or simply that the theoretical value assumes conditions (pure samples, ideal temperature) that were not met.

Signed Percent Error: Detecting Systematic Bias

The signed percent error reveals not just the magnitude of the error but its direction. If repeated trials consistently produce a negative signed percent error, your measurements are systematically low — suggesting a calibration issue, heat loss, evaporation, or another consistent source of error. If the sign alternates randomly, the error is more likely random (instrumental noise or human variation).

• Negative signed error — experimental value is less than theoretical. Example: a scale that consistently reads light, or a thermometer that reads below the true temperature.
• Positive signed error — experimental value exceeds theoretical. Example: a volume measurement that includes air bubbles, or a timer that stops late.

Tracking the sign of your percent error across multiple trials is one of the first steps in identifying and correcting systematic errors in experimental design.