Percent Error Calculator
Enter both values, then press Calculate. Percent error compares an observed measurement against the true (accepted) value.
A percent error calculator answers the question every lab report eventually asks: how far off was I, in a way that is fair to the size of the thing being measured? Being 0.11 out when measuring gravity is a small miss; being 0.11 out when measuring the mass of a paperclip is a catastrophe. Percent error puts both on the same honest scale by dividing the miss by the true value. The calculator above does the whole job — type your observed value and the true value, press Calculate, and you get the percent error with its complete working, the absolute and relative error, and a plain sentence telling you whether your measurement ran high or low.
I have graded enough lab reports to know that the formula is never the hard part. The marks disappear in the details: the wrong value on the bottom of the fraction, a minus sign kept or dropped at the wrong moment, and answers copied to thirteen decimal places from a machine when the measurements only justified two figures. This tool was built around exactly those three failure points, and this guide walks through each one.
The Percent Error Formula
Percent error compares an observed (measured) value against the true value — the accepted, known or theoretical one — and expresses the gap as a percentage of the truth:
percent error = |observed − true| ÷ |true| × 100
Three terms, three jobs:
| Term | Meaning | Also called |
|---|---|---|
| Observed value | What you actually measured | experimental, measured |
| True value | The known or accepted answer | accepted, theoretical, exact |
| |observed − true| | The size of the miss, in your units | absolute error |
The single most important habit: the true value goes on the bottom. Always. Dividing by your own measurement instead is the classic slip, and it quietly changes the answer — measure 10 against a true value of 11 and the error is 9.09%; put the 10 on the bottom by mistake and you would report 10%. The two are different because the formula is not symmetric. (A small aside for the careful reader: metrologists point out that a perfectly known "true value" never really exists, which is why formal writing prefers "accepted value". The mathematics is unchanged; the humility is the point.)
How to Calculate Percent Error, Step by Step
Take the classic first-year physics measurement: a pendulum experiment gives g = 9.7 m/s², and the accepted value is 9.81 m/s².
Step 1 — subtract. 9.7 − 9.81 = −0.11. Keep the sign for a moment; it tells you the direction of the miss.
Step 2 — take the absolute value. |−0.11| = 0.11. This is the absolute error, still wearing your units (m/s²).
Step 3 — divide by the true value. 0.11 ÷ 9.81 = 0.01122… This dimensionless number is the relative error.
Step 4 — scale to a percentage. 0.01122 × 100 = 1.12%. Your measurement of gravity was 1.12% too low. That final sentence — too low, not just "off" — is worth writing in the report, and the calculator above says it for you automatically.
This four-line layout is exactly what the calculator's step-by-step panel prints, with the fraction stacked the way you would write it on paper. Work the problem by hand first, then let the panel act as your marker.
Can Percent Error Be Negative?
This is the question that fills forums, and the answer is: it depends on which convention your course uses, and the calculator reports both so nobody is caught out.
The standard scientific definition uses the absolute value, so percent error is always positive — it measures the size of the miss, not its direction. That is the headline number this calculator shows. But many chemistry courses keep the sign, defining signed percent error as (observed − true) ÷ |true| × 100, so that a negative result means you measured low and a positive one means you measured high. You will find that signed value one line below the headline: for the gravity example it reads −1.12%, agreeing perfectly with the plain-language sentence above it. If your teacher wants the sign, use that row; if not, use the headline. They will never contradict each other here — which is more than can be said for some well-known calculators that show a negative headline and then a positive value in their own working.
What Is a Good Percent Error?
The honest answer is that there is no universal threshold — it depends entirely on what you measured and with what. Some working guideposts from years of lab teaching:
| Context | Typically considered reasonable |
|---|---|
| School lab with basic equipment | under 5–10% |
| University lab, decent instruments | under 1–5% |
| Analytical chemistry, calibrated glassware | under 1% |
| Quick estimation or field measurement | 10–20% can be acceptable |
What matters more than the number itself is whether you can explain it. A 4% error traced to a named cause — friction you could not eliminate, a stopwatch reaction time — earns more credit than an unexplained 1%. And if your percent error lands in the hundreds, suspect the arithmetic before the apparatus: the values are usually in the wrong boxes, which is precisely why this calculator watches for that pattern and offers to swap them for you.
Absolute Error and Relative Error
Percent error travels with two companions, and reports often ask for all three. The absolute error is the plain gap, |observed − true|, in the same units as the measurement — 0.11 m/s² in the gravity example. The relative error is that gap divided by the true value, left as a bare ratio: 0.0112. Multiply the relative error by 100 and you have the percent error; they are the same idea at different volumes. The calculator lists both under the headline — absolute error immediately, relative error behind the "More detail" button — so a report can quote whichever form the rubric demands.
Percent Error vs Percent Difference vs Percent Change
Three cousins, one family resemblance, and mixing them up is the quiet cause of many wrong answers, because each divides by a different thing:
| Measure | Divides by | Use when |
|---|---|---|
| Percent error | the true value | one value is known to be correct |
| Percent difference | the average of the two values | neither value is "the truth" — two experiments compared |
| Percent change | the original (earlier) value | one value came before the other in time |
The test is one question: is one of my two numbers the official answer? If yes, you want percent error and you are on the right page. If the two numbers are equals — two students measuring the same spring — that is percent difference. If time passed between them — a price last year and this year — that is percent change. Dedicated Monkza tools for those two are on the way; every calculator on the site is collected on the All Calculators page.
Why This Percent Error Calculator Is Built Differently
Having marked the reports, I built the tool I kept wishing students had used, and three habits set it apart from the usual suspects.
It rounds like a scientist, not like a float. Enter 10 against 11 elsewhere and you will be handed −9.0909090909091% — thirteen decimal places conjured from two-digit measurements. This calculator answers 9.09%, and then goes one better: it notices that a bare "10" hides its own precision (one significant figure or two?), says so, and shows you how to write it unambiguously. Copying thirteen decimals into a report is the fastest way to tell a marker you have not understood measurement; the whole point of the significant figures calculator next door is that an answer can never be more precise than the numbers that made it.
It catches the swapped-values mistake. The formula's commonest failure is putting the observed value on the bottom. When the answer comes out suspiciously enormous and swapping the boxes would produce a modest one, the calculator says so plainly and offers a one-tap swap. No other percent error calculator I have tested even notices.
It shows the working as a marker wants it. Formula, substitution with your own numbers, absolute error, division, percentage — five labelled lines with the fraction stacked properly, ready to be copied into a report. The answer also arrives as a sentence — "your measurement is 1.12% too low" — because a number with a direction is worth more than a number alone. Common true values (g, the speed of light, the density of water, Avogadro's number) sit one tap away, and there is not a single advertisement between you and any of it.
For the surrounding arithmetic — powers, roots, logarithms in the same homework — the scientific calculator is one tab away, and when your values arrive in forms like 6.022×10²³, this page accepts e-notation directly and the scientific notation calculator will convert anything the lab throws at you.
Worked Examples Worth Understanding
| Observed | True | Percent error | The lesson |
|---|---|---|---|
| 9.7 | 9.81 | 1.12% (low) | the everyday lab case |
| 2.53 | 2.70 | 6.3% (low) | density of aluminium, a classic |
| 105 | 100 | 5% (high) | overshooting counts the same way |
| 1.62×10³ | 1.60×10³ | 1.25% (high) | e-notation goes straight in |
| 100 | 2 | 4900% (!) | the swap detector's moment |
Frequently Asked Questions
How do you calculate percent error?
Can percent error be negative?
What is a good percent error?
What goes on the bottom of the fraction?
What if the true value is zero?
Is percent error the same as percentage error?
What is the difference between percent error and percent difference?
What is absolute error?
Why does this calculator show fewer decimal places than others?
Is this percent error calculator free?
Percent error is a small calculation with a big job: it turns "I was a bit off" into a number a scientist can defend. Keep the true value on the bottom, keep only the figures your measurements earn, and say which direction you missed in — the calculator above will hold you to all three habits while doing the arithmetic in a blink. When the same homework needs powers and roots, the scientific calculator is ready; when it questions how many digits to keep, the sig fig calculator settles it; and the whole free toolkit lives on the Monkza calculators page.