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Error Propagation Calculator

Calculate the uncertainty propagation for basic arithmetic operations.
What This Calculator Helps You Do
Use the inputs below to test scenarios, compare outcomes, and interpret the result before acting on it.

Error Propagation Calculator is designed to give you a fast answer, but it also provides supporting context such as formulas, worked examples, FAQs, and charts so the result is easier to validate.

For the best result, use realistic input values, review the assumptions in the explanation panels, and compare multiple scenarios if you are planning a decision based on the output.

Calculator
Enter your values
Analysis
Interpretation of the current calculator output

Enter values to see detailed analysis and insights.

How to Use

Step-by-step instructions
  1. 1Enter value A and its uncertainty.
  2. 2Enter value B and its uncertainty.
  3. 3Select the operation (Add, Subtract, Multiply, Divide).
  4. 4The calculator will show the result with propagated error.

Quadrature Sum

When combining measurements with uncertainties, errors propagate. For addition/subtraction, absolute errors add in quadrature. For multiplication/division, relative errors add in quadrature.
Addition: sqrt((dA)^2 + (dB)^2), Multiplication: |R|sqrt((dA/A)^2 + (dB/B)^2)

Variables:

A, BMeasured values
dA, dBAbsolute uncertainties

Example

Addition: (10 +/- 1) + (20 +/- 2)

Inputs:

A:10 +/- 1
B:20 +/- 2
Op:Add

Steps:

  1. 1.Value: 10 + 20 = 30
  2. 2.Error: sqrt(1^2 + 2^2) = sqrt(5) = 2.236
Result:
30 +/- 2.236

Frequently Asked Questions

Why quadrature?

Adding errors directly (linear sum) assumes the worst-case scenario where errors always reinforce each other. Quadrature (square root of sum of squares) assumes errors are independent and random.
In-depth guideBrowse Statistics calculators
Error Propagation Calculator Guide
Detailed usage notes, assumptions, mistakes to avoid, and related tools.

Error Propagation Calculator helps turn the available inputs into a result that is easier to check, compare, and explain. Calculate the uncertainty propagation for basic arithmetic operations.

Use this page together with 5 Number Summary Calculator when your question touches related assumptions in the same statistics workflow. For a nearby workflow, open 5 Number Summary Calculator.

Formula And Variables
How the calculator turns inputs into an answer.

Quadrature Sum is the main method behind this calculator. The equation is Addition: sqrt((dA)^2 + (dB)^2), Multiplication: |R|sqrt((dA/A)^2 + (dB/B)^2), and the calculator applies it consistently as you change the inputs.

The most important variables are: A, B is measured values, dA, dB is absolute uncertainties. Check those values first if the output looks higher or lower than expected.

How To Use The Result
What to compare before acting on the output.

The worked example on this page uses A = 10 +/- 1, B = 20 +/- 2, Op = Add and produces 30 +/- 2.236. Use that example as a quick check for the calculation flow before entering your own values.

For practical use, read the error propagation calculator result as a decision-support number. It is strongest when you compare two or more scenarios using the same units and assumptions.

Data Visualization And Analysis
Different chart views answer different questions about the same calculator output.

Best ways to read the charts

Use a bar chart when you need to compare separate result components, a line or area chart when the output changes across steps or time, and a pie-style distribution when every value is part of one total.

When the page shows multiple chart tabs, start with the overview, then check the ranking view to see which value drives the result most strongly.

What the analysis should tell you

Compare the average, range, highest value, lowest value, and dominant contributor before making a conclusion from the main number alone.

If one value contributes most of the total, test that assumption first. If values are spread evenly, the result is usually driven by the full input set rather than a single outlier.

Common Mistakes
  • Do not mix units unless the calculator explicitly converts them for you.
  • Avoid copying a result without checking whether the inputs describe the same time period, measurement system, or scenario.
  • If the answer looks surprising, change one input at a time so you can identify which assumption is driving the output.
When The Result May Be Inaccurate

The result can be inaccurate if inputs use mixed units, rounded source data, outdated rates, or assumptions that do not match the situation being modeled.

Run a second scenario with conservative inputs when the output will affect a purchase, project, health decision, academic answer, or financial plan.

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Additional Questions

How accurate is Error Propagation Calculator?

Error Propagation Calculator is accurate for the formula and inputs shown on the page. Real-world accuracy depends on whether the values you enter are complete, current, and measured in the expected units.

What should I check before using the error propagation calculator result?

Check the input units, review the formula section, compare the worked example, and run at least one alternate scenario if the result will support a decision.