Calculate absolute, relative, and percentage error between measured and actual values. Includes tolerance checking, error propagation, and visual comparison.
The Relative Error Calculator computes absolute, relative, and percentage error between a measured value and the true (actual) value. It also checks tolerance limits, propagates errors through mathematical operations, and visualizes the error with an interactive comparison chart.
Error analysis is essential in science, engineering, and quality control. Absolute error tells you how far off a measurement is in the original units, relative error normalizes this against the true value, and percentage error expresses it as a familiar percentage. Together they paint a complete picture of measurement accuracy.
This calculator goes beyond basic formulas by including tolerance pass/fail tables at multiple levels, error propagation for common operations (squaring, doubling, square root), significant figure analysis, and a visual comparison showing where your measurement falls relative to the tolerance band around the actual value. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Every measurement has some degree of error. Understanding and quantifying that error is critical for scientific reporting, quality control, and engineering specifications. This calculator provides a complete error analysis toolkit — from basic calculations to propagation and tolerance checking.
Students in physics and chemistry labs use it to compute experimental error. Engineers use the tolerance table to verify components meet specifications. Researchers use error propagation to understand how measurement uncertainty flows through their calculations.
Absolute Error = |Measured - Actual|. Relative Error = |Error| / |Actual|. Percentage Error = Relative Error × 100. Error Propagation (f=x²): δf = 2|x| × δx.
Result: Absolute Error = 0.3, Relative Error = 0.03, Percentage Error = 3.0%
Absolute: |10.3 - 10.0| = 0.3. Relative: 0.3 / 10.0 = 0.03. Percentage: 0.03 × 100 = 3.0%. This is within the 5% tolerance (3.0% < 5%).
Measurement errors fall into two categories: systematic and random. Systematic errors consistently bias measurements in one direction (e.g., a miscalibrated scale). Random errors scatter unpredictably and are reduced by averaging multiple measurements. Relative error captures the combined impact of both types.
When a measured value enters a calculation, its uncertainty propagates. The basic rules: for f = ax, δf = |a|δx. For f = x + y, δf = δx + δy. For f = xy, δf/f = δx/x + δy/y. For f = xⁿ, δf/f = |n|δx/x. These rules let you trace uncertainty through any calculation chain.
In manufacturing and quality control, tolerance defines the acceptable range around a nominal value. A 100Ω resistor with 5% tolerance can be anywhere from 95Ω to 105Ω. The tolerance table in this calculator checks your measurement against multiple common tolerance bands, instantly showing which specifications are met and which are violated.
Absolute error is the raw difference in measurement units (e.g., 0.3 grams). Relative error divides by the actual value to create a unitless ratio (e.g., 0.03). Relative error is better for comparing accuracy across different scales.
By convention, we usually report the absolute value (always positive). However, the signed error indicates direction: positive means overestimate, negative means underestimate. This calculator shows both.
Relative error is undefined when the actual value is zero (division by zero). In this case, only absolute error is meaningful. Some contexts use the measured value as the denominator instead.
When you use a measured value in further calculations, errors compound. For multiplication by a constant, relative error stays the same. For squaring, relative error doubles. For addition, absolute errors add.
It depends on the field. In chemistry labs, 1-5% is typical. In engineering, tolerances may be 0.1% or tighter. In social sciences, 5-10% may be acceptable. The tolerance table helps evaluate against multiple standards.
Significant figures indicate the precision of a measurement. More sig figs means more precision. The calculator counts the sig figs in your measured value to help assess whether the precision matches the accuracy.