Percent Error Calculator — Formula, Examples & Common Mistakes

Percent error measures how far your experimental result is from the accepted/true value — expressed as a percentage. It's the standard way to evaluate accuracy in chemistry labs, physics experiments, and engineering measurements.

The CalcHub Percent Error Calculator computes it instantly.

The Formula

Percent Error = |Experimental − Accepted| / |Accepted| × 100%

The absolute value bars (| |) mean the result is always positive — it doesn't matter whether your measurement was too high or too low.

Quick Examples

Accepted Value	Experimental Value	Absolute Error	Percent Error
100	98	2	2.0%
100	105	5	5.0%
9.81 m/s²	9.65 m/s²	0.16	1.63%
100°C	102.3°C	2.3	2.30%
3.14159	3.14	0.00159	0.051%
1,000	1,050	50	5.0%
36.46 g/mol	37.2 g/mol	0.74	2.03%

Common Lab Experiments

Experiment	Accepted Value	Typical Student Result	Typical % Error
Acceleration due to gravity	9.81 m/s²	9.5–10.1 m/s²	1–3%
Boiling point of water	100°C	99–101°C	0–1%
Speed of sound (20°C)	343 m/s	330–355 m/s	1–4%
Density of water	1.000 g/mL	0.97–1.03 g/mL	0–3%
Molar mass of NaCl	58.44 g/mol	57–60 g/mol	1–3%

What's an Acceptable Percent Error?

Field	Acceptable Error	Why
High school chemistry	< 5%	Student-grade equipment
University chemistry	< 2%	Better equipment and technique
Physics (mechanics)	< 3%	Friction and air resistance
Engineering	< 1%	Tighter tolerances
Pharmaceutical	< 0.5%	Safety-critical dosing
Analytical chemistry	< 0.1%	Precision instruments

Rule of thumb: Under 5% is generally good for student labs. Under 1% is excellent. Over 10% suggests a systematic error worth investigating.

Types of Error

Error Type	What It Is	Example
Absolute error	\	Measured − True\	Measured 9.65, true 9.81 → error = 0.16
Relative error	Absolute error / True value	0.16 / 9.81 = 0.0163
Percent error	Relative error × 100	0.0163 × 100 = 1.63%

Systematic vs Random Errors

Type	Description	Effect	Fix
Systematic	Consistent in one direction	All measurements shifted high or low	Calibrate equipment, fix technique
Random	Unpredictable fluctuations	Measurements scatter around true value	Take more measurements, average

If your percent error is consistently high in the same direction, you likely have a systematic error (e.g., uncalibrated scale, parallax error, impure reagents).

Sources of Error in Lab

Source	Effect	How to Minimize
Uncalibrated instruments	Systematic offset	Calibrate before use
Parallax error (reading scales)	Random/systematic	Read at eye level
Temperature fluctuations	Variable	Control lab temperature
Impure chemicals	Systematic	Use analytical grade
Human reaction time	Random	Use digital timers
Evaporation during heating	Systematic (mass loss)	Cover containers
Rounding intermediate values	Systematic	Round only final answer

How to Use the Calculator

1. Open the CalcHub Percent Error Calculator
2. Enter the accepted (true) value
3. Enter your experimental (measured) value
4. See: percent error, absolute error, and relative error

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Can percent error be negative?

The standard formula uses absolute values, so percent error is always non-negative. However, some instructors want signed percent error (positive = over, negative = under) to identify direction. Check your assignment requirements.

What if the accepted value is zero?

Percent error is undefined when the accepted value is zero (division by zero). In this case, use absolute error instead, or use a different metric like mean absolute deviation.

Is 0% percent error possible?

Theoretically yes — if your measurement exactly matches the accepted value. In practice, this is extremely rare with real measurements and might suggest you "adjusted" your data to match (which is not good science).

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Related Calculators

• Percentage Calculator — general percentage math
• Standard Deviation Calculator — spread of measurements
• Scientific Calculator — lab calculations
• Probability Calculator — statistical significance