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Scientific Tools · Updated October 21, 2026 · Reviewed by FormatFlow Editorial

Error Propagation Calculator

You can propagate measurement uncertainties through sums, products, powers or a custom function in your browser, then round the result to a correctly reported value and uncertainty.

Runs in your browserFree · No sign-up · No watermark
VALUES ± δ → RESULT ± δRuns in your browser
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Everything runs locally in this tab. No file is uploaded while the tool loads.

This tool runs in your tab. Nothing is uploaded and no copy is stored.

How files are handled

At a glance

Works with
VALUES ± δ → RESULT ± δ
Processing
In your browser
Price
Free, no account
Updated
October 21, 2026
All Scientific Tools

About Error Propagation Calculator

A measurement without an uncertainty is incomplete, and combining measurements changes how the uncertainties add up. A sum combines absolute uncertainties in quadrature, while a product or power combines relative uncertainties, which is why a small relative error in a large factor can matter more than a large absolute error in a small one.

This calculator handles sums and differences, products and quotients, powers and arbitrary functions. It assumes independent random errors, uses numerical partial derivatives for custom expressions, and reports the result with the uncertainty rounded to one significant figure (two when the leading digit is 1) and the value rounded to match.

What this tool does

The details that matter when you use Error Propagation Calculator for real work.

  • Four propagation modes

    Sums and differences, products and quotients, powers and custom functions each use the appropriate quadrature formula.

  • Numerical partial derivatives

    Custom functions are differentiated centrally at each variable, so no manual calculus is needed for f(x, y, …).

  • Correctly rounded reporting

    The uncertainty keeps one significant figure, or two when the leading digit is 1, and the value is rounded to the same decimal place.

  • Formula and working shown

    Every result lists the formula, the substituted values and the intermediate uncertainty so the arithmetic can be checked.

  • Clear validation

    Zero, negative or missing uncertainties, zero denominators and domain errors produce readable messages instead of a silent NaN.

  • Assumption stated plainly

    The tool says that quadrature assumes independent random errors, so correlated errors are not silently combined.

How to use Error Propagation Calculator

No account, no installation — the whole job happens in this browser tab.
  1. 01

    Choose the combination

    Pick sum or difference, product or quotient, power, or custom function depending on how the quantity is calculated.

  2. 02

    Enter values and uncertainties

    Type each value with its positive absolute uncertainty, adding rows for more terms.

  3. 03

    Or write the function

    For custom mode, enter f(x, y, …) and give every variable its value and absolute uncertainty.

  4. 04

    Check the working

    The formula, substituted numbers and, for custom functions, the partial derivatives are shown with the result.

  5. 05

    Copy the reported form

    Use the rounded value ± uncertainty in your report; the unrounded numbers stay visible for later calculations.

How this tool works

Works with
VALUES ± δ → RESULT ± δ
Processing
Client-side, in your browser. Nothing is uploaded.
Requirements
Chrome, Edge, Firefox or Safari · JavaScript enabled

Limitations worth knowing

  • Assumes independent random uncertainties; correlated or systematic errors need a covariance treatment that is not implemented.
  • Custom functions use numerical central differences, which are unreliable for non-smooth functions or extremely large and small values.
  • Uncertainties must be positive; exact values and asymmetric or non-Gaussian uncertainty distributions are not supported.

Privacy and file handling

The values, uncertainties and expressions you enter are handled with plain JavaScript inside your browser tab. Nothing is uploaded, logged or stored, and no request is made to a server while you calculate. Closing the page clears the inputs.

Read the full privacy policy

Error Propagation Calculator FAQ

Short, direct answers to the questions people ask before using this tool.
When do I combine absolute uncertainties and when relative ones?
For sums and differences, combine absolute uncertainties in quadrature. For products and quotients, combine relative uncertainties in quadrature and then scale back to an absolute uncertainty. A power combines relative uncertainties as |n| times δa/|a|.
Why is the uncertainty rounded to one significant figure?
That is the usual reporting convention: an uncertainty of 0.2236 is written as 0.2, while one starting with 1 keeps two figures so it does not lose too much information. The central value is then rounded to the same decimal place.
What assumption does combining in quadrature make?
It assumes the input errors are independent, random and roughly symmetric, so their variances add. Correlated or systematic errors do not cancel this way and need a covariance term, which this tool does not implement.
Why must the uncertainties be greater than zero?
The tool is built for measurements with a stated uncertainty, and the product and quotient formulas divide by the factor, so zero is not meaningful there. Exact values would need a different treatment.
How accurate are the numerical partial derivatives?
Custom functions use a central difference with a step of about 10⁻⁵ times the variable size, which is dependable for smooth functions. For a kink, a discontinuity or extremely large values the estimate can be poor, so check the result against the formula by hand.
Can I use a custom function with trigonometric functions?
Yes. The expression parser supports sin, cos, tan and their inverses plus logarithms, roots and exponentials, and trigonometric arguments are evaluated in radians.
Why does the calculator reject a zero factor or a zero base?
Relative uncertainty divides by the value, so a zero factor or base makes the formula undefined. The tool reports this explicitly rather than returning an infinite uncertainty.
Are my values and uncertainties uploaded?
No. The calculation runs with plain JavaScript in your browser tab; nothing is uploaded, logged or stored, and closing the page clears the inputs.

Background reading

Format guides that explain the trade-offs behind Error Propagation Calculator.