Significant Figures Calculator
Count the significant figures in a number, round to a target number of sig figs, or carry out a calculation with the correct sig-fig rule applied — and see exactly which input set the precision.
How to use this tool
Three modes: Count the sig figs in a measurement, Round a number to a chosen number of sig figs, or Calculate a · b with the rule that governs that operation.
What to enter
- Count / Round: any number, decimals or scientific notation (1.50e-3) welcome — trailing-zero intent is read from how you write it.
- Round: also the target number of significant figures.
- Calculate: two numbers and an operator (× ÷ + −).
Reading the result
Count flags the genuinely ambiguous case (trailing zeros with no decimal point). Calculate shows both the exact value and the sig-fig-correct value, and names the rule: × and ÷ keep the fewest significant figures; + and − keep the fewest decimal places.
Worked example
12.3 × 4.5 = 55.35, but each input has only 2 sig figs, so the reported answer is 55.
Result
Significant figures show how precisely a value is known. The last significant digit is the first uncertain one.
Methodology
Counting
All non-zero digits are significant; zeros between significant digits are significant; leading zeros never are. Trailing zeros are significant when a decimal point is present (120.0 → 4) but ambiguous without one (1500 → 2–4); the tool assumes they are not significant and flags it. In scientific notation every digit of the mantissa is significant.
Arithmetic
Multiplication and division: the result carries the fewest significant figures of any factor. Addition and subtraction: the result carries the fewest decimal places of any term. Rounding is applied once, to the final result.
Sources
- NIST Guide to the Expression of Uncertainty in Measurement (GUM).
- Standard general-chemistry significant-figure conventions.
Known limits
- Exact (counted) numbers and defined constants have unlimited significant figures and should not be used to limit the result.
- Calculate handles one operation (a · b); for a multi-step expression, round only at the very end, not between steps.