Significant Figures Calculator

What are significant figures?

Significant figures (sig figs, or significant digits) are the digits of a number that carry real information about its precision. A scale that reads 12.30 g tells you the mass to the nearest hundredth of a gram, so all four digits count. If the same mass were written 12.3 g, only three digits would count and the reading would be less precise.

The idea matters wherever numbers come from measurement. A result cannot honestly be more precise than the instrument and the least precise input behind it, so significant figures give a simple, shared way to show how much of a number can be trusted.

The rules for counting

1. Every non-zero digit is significant.
2. Zeros between non-zero digits are significant: 4,507 has four.
3. Leading zeros are never significant. They only locate the decimal point: 0.0032 has two.
4. Trailing zeros after a decimal point are significant: 0.003200 has four, and 100.0 has four.
5. Trailing zeros in a whole number with no decimal point are ambiguous. 1,200 is normally read as having two significant figures; a trailing point (1,200.) or scientific notation (1.200 × 10³) makes all four count.
6. Exact numbers, such as a count of 12 eggs or the 100 centimeters in a meter, have unlimited significant figures.

Counting significant figures with the calculator

Select Count sig figs, type the number and press Calculate. The first line gives the count and the second lists the significant digits in order, so 0.00120 returns 3 with the list 1, 2, 0. The sign is ignored, and a number written with a trailing decimal point such as 1200. counts every digit.

Numbers typed in e-notation are first turned into an ordinary number, which drops trailing zeros of the coefficient: 1.200e3 is read as 1200 and counts two figures. To keep the zeros, type the plain form with the decimal point instead, for example 1200. or 0.001200.

Rounding to a number of significant figures

1. Find the first non-zero digit. That is the first significant figure.
2. Count off the number of figures you want to keep.
3. Look at the next digit. If it is below 5, leave the last kept digit alone; if it is above 5, raise the last kept digit by one.
4. If the next digit is exactly 5 with nothing after it, apply your tie rule (see below).
5. Fill any dropped places before the decimal point with zeros so the size of the number is unchanged.

A tie happens when the dropped part is exactly half a unit in the last kept place, as in 2.5 rounded to one figure. Half away from zero (the usual school rule) gives 3. Half to even, favored in scientific work, gives 2, because it sends ties to the nearest even digit and so avoids a systematic upward drift when many values are rounded. Both rules agree on 3.5, which becomes 4. Use the Rounding rule option to choose.

Calculating with significant figures

In Calculator mode, enter two numbers (decimal or e-notation such as 1.23e+6), pick an operation and press Calculate. The rules it follows depend on the operation.

Addition and subtraction are limited by decimal places. Round the answer to the fewest decimal places among the inputs.

123.4 + 5.67 = 129.07 → 129.1123.4 has one decimal place, 5.67 has two, so the sum keeps one.

Likewise 100.25 − 0.5 = 99.75, which is reported as 99.8 because 0.5 has one decimal place.

Multiplication and division are limited by significant figures. Round the answer to the fewest significant figures among the inputs.

1.234 × 5.6789 = 7.0077626 → 7.0081.234 has four significant figures and 5.6789 has five, so the product keeps four.

In the same way 12.5 × 3.2 = 40.0 keeps two figures, and 4.7 ÷ 1.25 = 3.76 becomes 3.8. Do not round the inputs first; carry full precision through the calculation and round only the final answer.

Reading the results and the calculator’s limits

Each answer is shown three ways: the decimal value, e-notation (1.23e+2) and scientific notation (1.23 × 10²). Keep these points in mind when you use them.

• Rounding keeps the size of the number: the first result line is the rounded value itself, with its decimal point and any zeros needed to hold the place value. 123456 to three figures is 123000, 1234.5678 to six figures is 1234.57 and 0.0012345 to two figures is 0.0012. A number that has fewer figures than you ask for is shown as it is, without padding.
• Carrying a 9: when rounding up turns 9s into a 10, the carry moves into the next place. 99.95 to three figures is 100 and 0.0999 to two figures is 0.10. The e-notation lines drop trailing zeros, so 100 reads 1e+2 there.
• Negative numbers cannot be rounded in rounding mode; counting ignores the sign.
• Products and quotients may show padded zeros such as 6.300; read 6.300 as 6.3. When the integer part of the answer is already as long as the number of figures kept, the fraction is cut off rather than rounded, and a round-up that turns a run of 9s into a 10 is not carried, so check results that end in nines by hand.
• Operands are read as plain numbers, so a trailing zero after the decimal point (7.0) is dropped and counts as one figure.

For any value where the last digit matters, confirm it against the rules above. To write a result in the 1 to 10 format, use the scientific notation calculator.

Common mistakes

• Counting leading zeros. In 0.0032 the zeros only mark the position of the point.
• Mixing up decimal places and significant figures. Adding and subtracting use decimal places; multiplying and dividing use significant figures.
• Rounding at every step. Intermediate rounding accumulates error.
• Treating exact counts and definitions as if they limited precision.
• Dropping trailing zeros from a measured value: 2.50 g and 2.5 g are different claims about the scale.