Significant Figures Calculator

Count significant figures in a number, round to any number of them, and apply the arithmetic rules correctly.

Understanding the sig fig calculation

Significant figures encode measurement precision. Leading zeros never count, trailing zeros after a decimal point always do, and trailing zeros in a whole number are ambiguous unless written in scientific notation โ€” the calculator applies these rules to whatever you type.

The arithmetic rules differ by operation, which is the part students most often get wrong. Multiplication and division keep the fewest significant figures; addition and subtraction keep the fewest decimal places.

The default scenario, worked through

Worked through, a number of 0.004520, operation with the second number of None produces a significant figures of 4. Underneath, Rounded to your sig figs comes out at 0.00452 and Scientific notation at 4.52e-3. Change any field and every figure updates as you type.

Step by step

  1. Type your number exactly as written, including trailing zeros.
  2. Choose how many significant figures to round to.
  3. Add a second number and an operation to apply the arithmetic rules.

The calculation

multiply or divide: keep the fewest significant figures of the inputs add or subtract: keep the fewest decimal places of the inputs

FAQ

Do leading zeros count?
No. In 0.004520 the three leading zeros are placeholders; the significant figures are 4, 5, 2 and 0 โ€” four in total.
Do trailing zeros count?
After a decimal point, yes. In a whole number like 1500 they are ambiguous โ€” write 1.50 ร— 10ยณ to make it explicit.
Why do the rules differ between operations?
Because multiplication propagates relative error while addition propagates absolute error, which map onto significant figures and decimal places respectively.