Percent Error Calculator - Experimental vs Accepted Value

A percent error calculator compares a measured (experimental) number to a known accepted or theoretical value and reports how far off the measurement is as a percentage of that accepted value. The usual lab formula is:

The default on this page is a small gravity-style miss: experimental 9.8 against accepted 9.81. Absolute error is 0.01. Percent error is 0.01 / 9.81 × 100 ≈ 0.1019%. That is a tight measurement relative to the standard; the same 0.01 gap against an accepted value of 0.5 would be a 2% error. Percent error scales the miss by the size of the true value, which is why labs quote it instead of only the raw difference.

This free online percent error tool also prints signed percent error (no absolute value on the numerator) and absolute error in the same units as the inputs. An accepted value of zero is rejected because the formula divides by it. Everything runs in the browser; nothing is uploaded.

1. Enter the experimental value - what you measured, observed, or computed from lab data.
2. Enter the accepted value - textbook constant, calibrated standard, or theoretical prediction. Zero is not allowed.
3. Read percent error (magnitude), signed percent error (direction), and absolute error. Copy the percent for a notebook. Inputs are stored locally for up to 30 days.

Note: this is not percent change of a price, and it is not percent difference between two untrusted measurements. For those, use the percentage calculator. For a mean of replicates before you compare to a standard, use the average calculator.

Plug in experimental E = 9.8 and accepted A = 9.81:

• Difference E − A = 9.8 − 9.81 = −0.01
• Absolute error |E − A| = 0.01
• |A| = 9.81
• Percent error = 0.01 / 9.81 × 100 = 0.101936799…%
• Signed percent error = (−0.01) / 9.81 × 100 = −0.101936799…%

The negative signed error means the measurement sits below the accepted value. Many lab rubrics still want the unsigned percent error and a separate sentence (“low by 0.01 m/s²”). This page gives both so you do not have to re-derive the sign from a magnitude.

Second example - titration:

You find 0.102 M; the standard is 0.100 M. Absolute error 0.002. Percent error = 0.002 / 0.100 × 100 = 2%. Signed error is +2% (high). Same 0.002 M miss against a 1.00 M standard would be only 0.2%. Always divide by the accepted concentration, not by your measured one.

Third example - overestimate:

Experimental 105, accepted 100. Percent error 5%. Signed +5%. A student who divides by 105 instead of 100 reports about 4.76% and is using the wrong denominator. The definition is relative to the accepted value.

The experimental value is yours: a stopwatch average, a buret reading converted to molarity, a calorimeter ΔT turned into heat, a measured period of a pendulum. It includes random scatter and systematic bias. The accepted value is the number the community or the instructor treats as true for the comparison: g = 9.81 m/s² at that latitude (or 9.8 if the handout says so), a certified concentration, a manufacturer’s density, a value from a data booklet.

Percent error always divides by the accepted value. Swapping the two fields answers a different, usually wrong, question. If you have two measurements and no standard, you want percent difference (often |x1 − x2| / ((|x1| + |x2|)/2) × 100), which this page does not compute. If you are tracking how a KPI moved from last month to this month, that is percent change on the percentage calculator, dividing by the starting amount, not by a “true” value.

Units must match. 9.8 m/s² versus 981 cm/s² is not a 99% error; it is a unit mistake. Convert first. This calculator does not know units - it only sees two numbers.

Relative error without the ×100 is just percent error as a fraction: 0.001019 instead of 0.1019%. Some papers quote that. This page always reports the percent form. Absolute error is what you need when A is zero or when the instructor wants “off by 0.01 m/s²” in SI units. Percent error is undefined at A = 0; we refuse to print Infinity.

The classroom formula takes absolute values, so the number you circle on a lab sheet is ≥ 0. Signed percent error on this page is negative when E < A. If the rubric says “percent error cannot be negative,” copy the unsigned line. If the rubric asks whether you were high or low, use the signed line or the sign of (E − A).

When the true value is actually zero - a residual that should vanish, a net charge of an isolated system, a deviation from a null - percent error is the wrong statistic. Report absolute error, an RMS residual, or a domain-specific tolerance. Do not pick a tiny fake A to force a huge percent. This calculator will not invent a denominator.

Dividing by the experimental value. Forgetting × 100 and reporting 0.001 as “0.001%.” Mixing units (mL vs L, cm vs m). Using a rounded accepted value of 10 for g while the handout said 9.81, then wondering why the class mean is “off.” Calling percent difference percent error when both numbers came from your own runs. Quoting six digits of percent error when the measurements had two significant figures - the formula does not add precision.

IEEE floating-point is used here, same as any JavaScript number. 9.8 − 9.81 may be 0.010000000000000675 internally before we format. For this default the displayed percent is reliable well past a lab’s sig figs. It is not a computer algebra exact fraction. Huge or tiny values can underflow or overflow like any IEEE divide.

This page does not propagate uncertainty, does not compute t-tests against A, and does not decide whether an error is “good.” A 5% error can be excellent in a coffee-cup calorimeter and unacceptable in an analytical titration. The number is a comparison, not a grade. Class rubrics that say “under 5% is full credit” are pedagogy, not physics; two labs with the same percent error can have opposite signed errors and different stories.

Propagation of error from ΔL and ΔT into g = 2L/t² is a different homework question. Compute g first, then type that g as experimental against 9.81. Do not type Δg / g × 100 into this box and call it percent error unless Δg really is |E − A|. Relative uncertainty and percent error versus a standard are cousins, not twins. If A came from your own previous lab, you are closer to percent difference - say so in the write-up.

Accuracy is closeness to the accepted value - that is what percent error measures for a single reported number. Precision is how tightly repeats cluster, even if they all miss the truth together. A balance that always reads 0.20 g high can be precise (tiny scatter) and inaccurate (large percent error against a 5.00 g standard: 0.20/5.00 × 100 = 4%). Averaging imprecise trials can still land near A by luck; a small percent error on a mean does not prove a tight method.

Report both. Percent error of the mean versus A, and a spread (range or standard deviation) among trials. This page only does the first of those once you type the mean as “experimental.” It will not see that your three periods were 1.92 s, 2.01 s, and 2.40 s if you only paste 2.11. Outliers that you drop must be mentioned; silently omitting the 2.40 s trial to shrink percent error is not analysis.

Systematic error (a meter stick that starts at 2 mm, a clock that runs slow) moves E in one direction and shows up in signed percent error. Random error scatters around and may cancel in a mean. A signed error of −12% with tiny scatter screams calibration, not “we need more trials.” A signed error near zero with huge scatter screams that the mean is not yet trustworthy even if percent error looks pretty.

The default 0.1019% has four digits because IEEE division produced them, not because 9.8 had four significant figures. 9.8 has two significant figures if it was read from a cheap analog meter; then percent error should be stated as about 0.10% or even 0.1%, and the interesting sentence is “we agree with 9.81 to the digits we measured.” Do not copy twelve digits from this display into a table that lists g as 9.8.

Absolute error 0.01 m/s² next to accepted 9.81 m/s² already tells a reader the miss is in the hundredths place. Percent error is the relative view: useful when comparing a density experiment (accepted 2.70 g/cm³, experimental 2.61 → |2.61−2.70|/2.70×100 ≈ 3.3%) to a timing experiment with different units. You cannot compare 0.09 g/cm³ to 0.01 m/s²; you can compare 3.3% to 0.10% as relative misses, with the caveat that the methods’ difficulties differ.

If the accepted value is itself rounded (handout prints g = 9.8, you measured 9.81), percent error against 9.8 is |9.81−9.8|/9.8×100 ≈ 0.10%, and you are mostly measuring the handout’s rounding. Use the most precise accepted value the instructor named. If they named 9.8, use 9.8, not CODATA 9.80665, unless the lab is about that constant.

Density of water near 1.00 g/mL, melting point of ice at 0.00 °C (accepted zero - percent error undefined; use absolute error in °C), and a 25.00 mL volumetric flask filled to 24.82 mL (0.72% low) are all fair uses. A “percent error” on a survey Likert score against a national average is stretching the lab definition; say percent difference or percent change instead.