Significant Figure Arithmetic Calculator
Add, subtract, multiply or divide entered decimal measurements with exact rational arithmetic and operation-specific significant-figure rounding.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Preserve precision in input strings, compute the exact rational result and round once under the selected operation’s conventional rule.
Add/subtract: coarsest final decimal place; multiply/divide: fewest input significant figures
Worked example
12.3+0.45=12.75 rounds to 12.8 because tenths is the coarsest final place. 1.20×3.0=3.600 rounds to 3.6 because the limiting input has two significant figures.
Assumptions and input details
Up to 40 digits per input and scientific exponents −50 through 50. Plain whole-number trailing zeros are placeholders unless a decimal point or exponent makes them explicit: 1200 has two significant figures, while 1200. and 1.200e3 have four. No input is treated as an exact counted constant. Exact halves round away from zero, and zero-product precision is labelled separately. These classroom rules do not replace uncertainty propagation.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Decimal inputs and arithmetic use exact integer rational values. The final result is rounded once under the documented significant-figure convention, with exact halves away from zero. This describes input precision, not a propagated measurement uncertainty.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Write a number in normalized scientific notation, choose significant digits and inspect its coefficient, exponent and rounded decimal value.
Propagate absolute measurement bounds through addition, subtraction, multiplication or division. See a guaranteed enclosing interval rather than a statistical confidence interval.
Propagate independent standard uncertainties through a sum, difference, product or quotient using first-order sensitivities.
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