Percent Error Calculator: Formula & Steps

Using the Percent Error Calculator (Precision Lab)

Enter observed and true values above. Results and the Accuracy Visualization update live. Use the Formatting options for significant figures and scientific notation; see the article below for the formula and when to use percent vs absolute error.

At a glance

Observed vs true

Observed = your measurement; true = accepted or reference value. Percent error is undefined when true is 0.

Always positive vs directional

Always positive shows magnitude only; directional keeps the sign (over- vs under-estimate).

Precision gauge

Color bar: green (≤1%), yellow (1–5%), orange (5–10%), red (>10%). Use as a rough reference; standards vary by field.

Logic Trace

Step-by-step breakdown: absolute error → divide by true → × 100. Helps with homework and lab write-ups.

Percent Error Calculator: Formula, Steps & When to Use It

Free percent error calculator with step-by-step Logic Trace. Enter observed and true values—get percent error and absolute error. Handles division by zero; optional signed or always-positive. Trusted by students and educators for labs, quality control, and science coursework. No sign-up; all calculations run locally.

What This Calculator Does and Who It’s For

Who it’s for

Students in physics, chemistry, or engineering labs; anyone reporting experimental error or comparing a measurement to a reference; quality control and calibration. Commonly used when instructors ask for “percent error formula with example” or “absolute error vs percent error.”
Trust and scope

All calculations run in your browser; no data is sent to any server. The formula and edge cases (e.g. true value zero) are handled transparently so you can rely on the result and the displayed steps.

This percent error calculator computes percent error and absolute error from an observed (measured) value and a true (accepted) value. It’s built for quick, accurate how to calculate percent error workflows: enter two numbers, choose always-positive or directional error, and get results with significant-figure and scientific-notation options. The Logic Trace shows each step of the calculation, and the Accuracy Visualization bar shows how far observed and true values differ—so you can verify your work or use it as a percent error calculator with steps for lab reports and homework.

Percent Error Formula and Absolute Error

The percent error formula is:

\text{Percent Error} = \frac{\text{Observed} - \text{True}}{\text{True}} \times 100

The absolute error is simply Observed − True. Percent error expresses that difference relative to the true value, so it’s scale-independent—you can compare accuracy across different magnitudes. For a single positive number (common in lab reports), use the absolute value:

\frac{|\text{Observed} - \text{True}|}{|\text{True}|} \times 100

This calculator offers both: toggle “Always positive” for the absolute-value form, or “Directional” to keep the sign (positive when observed > true, negative when observed < true)

When the True Value Is Zero

When the true value is 0, the denominator in the percent error formula is zero, so percent error is undefined. This tool displays “Error: Division by Zero” and does not compute a percent in that case; the absolute error (Observed − True) is still shown. In practice, use a different reference or report only absolute error when the true value is zero.

Interpreting the Precision Gauge and Accuracy Visualization

The precision gauge is a quick visual: green for percent error ≤1%, yellow for 1–5%, orange for 5–10%, red for >10%. Standards vary by discipline—treat it as a rough guide and check your course or protocol. The Accuracy Visualization (comparison bar) plots the true value (green) and observed value (blue) on a number line; the distance between them is proportional to the absolute error, and the shaded “error bridge” shows underestimation (amber) or overestimation (red) when directional mode is on. Together with the Logic Trace, you get a full, auditable view of how the percent error was computed.

Percent Error Calculator FAQ

? How do you calculate percent error?

Use the formula

\text{Percent Error} = \frac{\text{Observed} - \text{True}}{\text{True}} \times 100

Enter your measured value (observed) and the accepted value (true) in the calculator above; it returns percent error and absolute error, with a step-by-step Logic Trace so you can see each step of the calculation. You can choose always-positive (absolute value) or signed (directional) error

? What if the true value is zero?

Percent error is undefined when the true value is 0 because the formula requires division by zero. This calculator shows “Error: Division by Zero” in that case and still reports the absolute error (Observed − True). For zero reference values, report absolute error only or use a different reference.

? What is the difference between percent error and absolute error?

Absolute error is the raw difference (Observed − True). Percent error is that difference as a percentage of the true value, so it’s scale-independent—you can compare accuracy across different magnitudes. The calculator shows both and the Logic Trace breaks down the three steps: absolute error, division by true value, then × 100.

? When should I use absolute value vs directional percent error?

Use always positive when you only care about “how far off” (e.g. lab reports, quality control). Use directional when the sign matters—e.g. overestimate vs underestimate, or when combining errors. The tool’s toggle switches between the two; the Accuracy Visualization bar and Logic Trace update accordingly.

? What is a good percent error?

It depends on the field. In many science and engineering contexts, under 5% is acceptable and under 1% is often excellent. The calculator’s precision gauge (green → red) is a rough guide; check your course, protocol, or industry standard for your use case.

Precision Lab

Formatting