Percent Error Calculator

Compare an experimental or measured value with the accepted or true value and instantly find the percent error.

Percent Error

True / Accepted Value

Measured / Experimental Value

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Percent Error: Definition, Formula, and Measurement Insights

Percent error measures how far a measured or experimental value is from a true or accepted value, expressed as a percentage of the true value.

This guide mirrors your other calculator pages with structured boxes, examples, tables, pitfalls, and practice problems, all focused on percent error in labs, experiments, and real measurements.

What Is Percent Error?

Percent error quantifies the relative difference between an experimental value and the accepted true value.

Formal definition

Percent error = |Experimental − True| / |True| × 100%

True value: Accepted, theoretical, or standard value.
Experimental value: Measured value from an experiment or observation.
Absolute difference: The size of the error, ignoring sign.

Example 1: Simple percent error
True value: 100, experimental: 95.
Error = |95 − 100| = 5; percent error = 5/100 × 100 = 5%.

Example 2: Overshoot
True value: 50, experimental: 53.
Error = |53 − 50| = 3; percent error = 3/50 × 100 = 6%.

True	Experimental	Absolute Error	Percent Error
100	95	5	5%
80	76	4	5%
50	53	3	6%
10	9.5	0.5	5%
25	24	1	4%

Percent Error Formula and Variants

The standard percent error formula uses the true value as the base, but some fields use signed error or alternate bases.

Standard (absolute) percent error

Percent error = |E − T| / |T| × 100%
where E is experimental, T is true.

Example:
T = 32.0, E = 31.2.
Error = |31.2 − 32.0| = 0.8; percent error = 0.8/32 × 100 ≈ 2.5%.

Signed percent error

Signed % error = (E − T)/T × 100%
Positive = overshoot, negative = undershoot.

Example:
T = 100, E = 105.
Signed error = (105 − 100)/100 × 100 = +5%.

Relative vs absolute error

Absolute error = |E − T| (same units as measurement).
Relative error = |E − T| / |T| (dimensionless), percent error is relative error × 100%.

Quantity	Formula	Units	Use
Absolute error	\|E − T\|	Same as measured	Raw difference
Relative error	\|E − T\| / \|T\|	None	Scaled difference
Percent error	Relative error × 100%	%	Easy comparison

Step-by-Step Examples

These examples show how to compute percent error in laboratory and real-life measurement situations.

Example 1: Mass measurement

A standard weight is 50.0 g, but a scale reads 49.1 g. Find the percent error.

Solution:
Step 1: T = 50.0, E = 49.1.

Step 2: Absolute error = |49.1 − 50.0| = 0.9 g.

Step 3: Percent error = 0.9/50.0 × 100 = 1.8%.

Answer: 1.8% error.

Example 2: Length measurement

The true length of a rod is 1.000 m; a measurement gives 0.985 m.

Solution:
Step 1: T = 1.000, E = 0.985.

Step 2: |E − T| = |0.985 − 1.000| = 0.015 m.

Step 3: Percent error = 0.015 / 1.000 × 100 = 1.5%.

Answer: 1.5% error.

Example 3: Overshoot in timing

A reaction is known to complete in 2.50 s, but a stopwatch reading is 2.65 s.

Solution:
Step 1: T = 2.50, E = 2.65.

Step 2: |E − T| = 0.15 s.

Step 3: Percent error = 0.15 / 2.50 × 100 = 6%.

Answer: 6% error.

Where Percent Error Is Used

Percent error is widely used in scientific experiments, engineering tolerances, and any situation where accuracy of measurements matters.

🔬 Laboratory Experiments

Chemistry and physics labs use percent error to compare experimental results to theoretical predictions or reference values.

⚙️ Engineering and Manufacturing

Engineers check if parts are within acceptable percent error ranges relative to design dimensions or performance targets.

📏 Instrument Calibration

Devices like thermometers, pressure gauges, and scales are calibrated by measuring percent error against standards.

📊 Data Validation

Percent error helps evaluate the accuracy of models or simulations by comparing predicted values to observed data.

💻 Sensors and IoT

In embedded systems, percent error is used to judge the quality of sensor readings under different conditions.

📈 Forecasting

Forecast percent error indicates how close predictions (like demand or weather) are to actual outcomes.

Common Mistakes with Percent Error

Many students and professionals misapply the formula or choose the wrong base, leading to misleading error values.

❌ MISTAKE 1: Dividing by the wrong value
Using experimental value in the denominator instead of the true value changes the meaning.
✅ Always divide by the true or accepted value when computing percent error (unless a specific field defines it differently).

❌ MISTAKE 2: Forgetting absolute value
Dropping the absolute value can produce negative “percent error”.
✅ Use |E − T| for standard percent error so the result is always non‑negative.

❌ MISTAKE 3: True value equal to zero
Dividing by zero makes the expression undefined; percent error cannot be computed when the true value is zero.
✅ If T = 0, use absolute error alone or another relative measure suitable for your context.

❌ MISTAKE 4: Confusing percent error with percent difference
Percent difference compares two experimental values instead of experimental vs true.
✅ Use the correct formula depending on whether you compare to a reference or between two measurements.

Related Concept: Percent Difference

Percent difference is often used when there is no known true value, and you instead compare two experimental measurements.

Percent difference formula

Percent difference = |E₁ − E₂| / ((|E₁| + |E₂|)/2) × 100%

Example:
Two measurements of the same quantity: 9.8 and 10.1.
Average = (9.8 + 10.1)/2 = 9.95; difference = |9.8 − 10.1| = 0.3.
Percent difference = 0.3 / 9.95 × 100 ≈ 3.02%.

Measure	Formula	Use Case
Percent error	\|E − T\| / \|T\| × 100%	Compare measurement to accepted value
Percent difference	\|E₁ − E₂\| / average × 100%	Compare two experimental values

Practice Problems with Solutions

Use these to test your understanding of percent error, then check your answers with the calculator above.

Basic Level

Problem 1: True value is 25.0; experimental value is 24.0. Find the percent error.

Show Solution

|24.0 − 25.0| = 1.0; 1.0/25.0 × 100 = 4% error.

Problem 2: A standard resistance is 100 Ω; measured resistance is 103 Ω.

Show Solution

|103 − 100| = 3; 3/100 × 100 = 3% error.

Intermediate Level

Problem 3: A density is known to be 1.00 g/mL. A student measures 0.96 g/mL. Find percent error.

Show Solution

|0.96 − 1.00| = 0.04; 0.04/1.00 × 100 = 4% error.

Problem 4: True acceleration due to gravity is 9.81 m/s², experiment gives 9.65 m/s².

Show Solution

|9.65 − 9.81| = 0.16; 0.16/9.81 × 100 ≈ 1.63% error.

Advanced Level

Problem 5: The accepted wavelength of a light source is 650 nm. A device measures 642 nm. What is the percent error, and is it an underestimation or overestimation?

Show Solution

|642 − 650| = 8; 8/650 × 100 ≈ 1.23% error.
Since 642 < 650, it is an underestimation.

Problem 6: A reference voltage is 5.00 V. A sensor reports 4.88 V. If your lab requires less than 3% error, does this reading pass the requirement?

Show Solution

|4.88 − 5.00| = 0.12; 0.12/5.00 × 100 = 2.4% error.
2.4% < 3%, so the reading passes the requirement.