Sig Fig Calculator

How to use the calculator

1. Pick a mode. Count tells you how many significant figures a number has. Round keeps the number of figures you choose. Arithmetic combines two numbers, A and B, with +, −, × or ÷.
2. Type the number as it appears in your data. Decimals (0.004050, .5, 1200.), grouping commas (-1,234.50) and scientific notation (4.050e-3, 6.02 × 10^23, 6.02x10^23) all work. Don't drop any zeros, because they are what gets counted.
3. Read the result and any note. Count mode adds the significant digits, the decimal places and an unambiguous scientific form; arithmetic mode adds the unrounded answer and the rule applied.

The significant figure rules used

In NIST's SI guide, a digit is significant if it is required to express the numerical value of a quantity. Its example is 1.200 km, where the two final zeros count, because otherwise the value would be written 1.2 km. The calculator applies the usual counting rules:

• Every nonzero digit counts, and so does every zero between nonzero digits (1.0070 has 5).
• Leading zeros never count (0.004050 has 4: the digits 4050).
• Trailing zeros count when a decimal point is written: 12.30 and 100.0 have 4, and so does 1200. with a final point.
• Trailing zeros in a whole number with no decimal point are ambiguous: 1200 could have 2, 3 or 4, so the result reads "2–4".
• In scientific notation only the mantissa counts: 6.02 × 10^23 and 1.20e3 both have 3.

Zero has no significant figures; its precision is shown by the decimal places instead (0.00 has 2). When rounding, a dropped 5 rounds up in magnitude, so -0.0004450 to 2 figures is -0.00045. In arithmetic, addition and subtraction keep the coarser last decimal place of the two numbers, while multiplication and division keep the smaller number of significant figures. An ambiguous whole number is read conservatively, so 1200 counts as 2 figures. Logarithms and uncertainty propagation aren't modeled. Your teacher or textbook may word these rules differently.

Worked examples

1. Counting zeros in a lab reading

A balance shows 0.004050 g. Count mode returns 4: the leading zeros only place the decimal point; the trailing zero was measured. The scientific form is 4.050 × 10⁻³, with 6 decimal places. Typing 1200 returns "2–4", while 1200. returns 4 (1.200 × 10³).

2. Multiplying in a gas-law problem

8.314 × 298.15 gives an unrounded 2478.8191. 8.314 has 4 significant figures and 298.15 has 5, so the answer keeps 4: 2479. In the same way, 0.004050 × 2.31 = 0.0093555 is reported as 0.00936 (3 figures, set by 2.31), and 2.00 ÷ 3.00 = 0.667.

3. Adding and subtracting measurements

In the last row, 50.0 is known only to the tenths place, so the difference keeps just 1 significant figure.

Reading the notes

• Ambiguous: a whole number with trailing zeros. Write 1200. or 1.200e3 if all four figures are real.
• Ambiguous result: 1195 to 3 figures is 1200, which can't show its third significant zero, so use the scientific form, 1.20 × 10³. By contrast, 99.96 to 3 figures appears as "100.": the trailing point marks the units zero as significant.
• Padded: you asked for more figures than were written, e.g. 2.5 to 4 gives 2.500. That adds no real precision.
• Ambiguous input: an operand such as 1200 was read as 2 figures, so 1200 + 35 = 1200 and 10 ÷ 3.0 = 3.