Significant Figures Calculator (Sig Fig Counter and Rounder)
This calculator counts the significant figures in any number, rounds a value to a given number of sig figs, and handles arithmetic (addition, subtraction, multiplication and division) applying the correct significant figure rules at each step. Enter your number in the first field, choose how many sig figs you want, and pick a mode. Results update instantly with a full show-your-work panel.
What are significant figures?
Significant figures (sig figs) are the digits in a number that carry meaningful information about its precision. When you measure something with a ruler that reads to the nearest millimetre, your result is only known to that precision, and every digit you write should reflect that. Non-zero digits are always significant. Zeros between non-zero digits (captive zeros, such as the zero in 1.006) are always significant. Leading zeros, the zeros to the left of the first non-zero digit (as in 0.0042), are never significant - they only mark the decimal place. Trailing zeros are trickier: if a decimal point is present (2.500), every trailing zero is significant because it was deliberately written to show precision; without a decimal point (1200), trailing zeros are ambiguous and it is better to use scientific notation to be explicit.
Sig fig rules for arithmetic
Two separate rules govern how precision propagates through calculations. For addition and subtraction, the result is rounded to match the operand with the fewest decimal places (not the fewest sig figs). For example, 12.52 + 349.0 + 8.24 = 369.76, which rounds to 369.8 because 349.0 has only one decimal place. For multiplication and division, the result has as many significant figures as the operand with the fewest significant figures. For example, 3.14 x 2.5 = 7.85, which rounds to 7.9 because 2.5 has only two sig figs. An important tip: in multi-step calculations, carry extra digits through each intermediate step and round only the final answer - rounding too early introduces rounding errors that compound.
Scientific notation and sig figs
Scientific notation is the clearest way to express a number with an unambiguous number of sig figs. Writing 1.200 x 10^3 unambiguously shows four sig figs, whereas "1200" alone is ambiguous. The coefficient (mantissa) of a number in scientific notation contains exactly the digits that are significant. Converting between standard and scientific notation does not change the number of sig figs - only the way the precision is expressed. This calculator accepts numbers written with an "e" or "E" in place of the "x 10^" part (for example, 1.200e3 is the same as 1.200 x 10^3).
When sig figs matter most
Significant figures are central to chemistry, physics, engineering and any scientific field where measurements are made with instruments of limited accuracy. Reporting too many sig figs implies a precision you do not have; reporting too few discards information. In laboratory work, the precision of your answer should match the precision of your least precise measurement. In everyday contexts such as personal finance or cooking, exact numbers and definitions have infinite sig figs and you round for readability rather than to reflect measurement error.
Significant figures rules at a glance
| Type of digit | Significant? | Example | Sig figs |
|---|---|---|---|
| Non-zero digits | Yes | 3.14 | 3 |
| Zeros between non-zero digits (captive zeros) | Yes | 1.006 | 4 |
| Leading zeros (before first non-zero digit) | No | 0.0042 | 2 |
| Trailing zeros with a decimal point | Yes | 2.500 | 4 |
| Trailing zeros without a decimal point | Ambiguous | 1200 | 2 or 3 or 4 |
| Exact numbers (counted, defined) | Infinite | 12 eggs (exactly) | infinite |
Quick reference for identifying which digits in a number are significant.
Frequently asked questions
How many significant figures does 0.0042 have?
Two. The leading zeros (0.00) simply indicate the decimal position and are not significant. The first significant digit is 4, and the 2 that follows is also significant, giving exactly two sig figs.
Are trailing zeros significant?
It depends on whether a decimal point is present. In 2.500, the trailing zeros are significant because the decimal point signals that they were measured rather than estimated - this number has four sig figs. In 2500 (no decimal point), the trailing zeros are ambiguous: the number could have two, three or four sig figs. Use scientific notation (2.500 x 10^3) or a decimal point (2500.) to make the precision explicit.
What is the sig fig rule for addition and subtraction?
For addition and subtraction, round the result to the same number of decimal places as the operand with the fewest decimal places. For example, 5.1 + 2.36 = 7.46, but since 5.1 has only one decimal place, you round to 7.5.
What is the sig fig rule for multiplication and division?
For multiplication and division, the result has as many significant figures as the operand with the fewest significant figures. For example, 4.56 x 1.4 = 6.384, but since 1.4 has only two sig figs, the answer rounds to 6.4.
How do I express 1200 with exactly three significant figures?
Write it in scientific notation as 1.20 x 10^3. That unambiguously signals three sig figs because the trailing zero in the coefficient is after the decimal point. Alternatively, some texts allow a decimal point at the end (1200.) to indicate all four digits are significant, but this notation is non-standard.
Do exact numbers have significant figures?
Exact numbers - those that are defined or counted rather than measured - are considered to have infinitely many significant figures and never limit the precision of a calculation. The 2 in the circumference formula C = 2 times pi times r, or the count "12 eggs in a dozen", are exact. Only measured quantities limit your sig figs.
Should I round at every step of a multi-step calculation?
No. Round only at the final step. Rounding intermediate results introduces rounding errors that can accumulate significantly over several steps. Carry at least one or two extra digits through each intermediate calculation and round the final answer to the appropriate number of sig figs.