Significant Figures Calculator

Significant figures are the digits in a measured number that carry real information about its precision. This tool counts them in any number you type, highlights which digits count and explains the rule behind each one. It also rounds a number to however many significant figures you choose, and it adds, subtracts, multiplies or divides two measurements and rounds the answer the way chemistry and physics courses expect.

It accepts ordinary decimals, numbers with thousands separators, and scientific notation written as 4.05e-3, 4.05 × 10^-3 or with superscript digits. When trailing zeros in a whole number make the count ambiguous, it says so and shows the answer in scientific notation, which is never ambiguous.

• Nonzero digits are always significant: 45.872 has five.
• Captive zeros between nonzero digits are significant: 10.05 has four.
• Leading zeros only place the decimal point and never count: 0.00340 has three.
• Trailing zeros after a decimal point count, because someone chose to write them: 2.50 has three.
• Trailing zeros in a whole number with no decimal point are ambiguous: 1200 could have two, three or four. Writing 1200. or 1.200 × 10³ makes it clear.
• Exact numbers, such as counted objects or defined conversions like 100 cm in 1 m, have unlimited significant figures and never limit a result.

Adding and subtracting: round the answer to the decimal place of the least precise number. 12.11 + 18.0 = 30.11, but 18.0 is only known to tenths, so the answer is 30.1.

Multiplying and dividing: keep as many significant figures as the input with the fewest. 4.56 × 1.4 = 6.384, but 1.4 has two significant figures, so the answer is 6.4. Likewise 25.0 ÷ 3 gives 8 if the 3 is a measurement; if it is an exact count, keep three figures instead.

Multi-step work: carry at least one or two extra digits through intermediate steps and round only the final answer, or rounding errors build up. Rounding 3.14159 to three figures gives 3.14.

A measurement is only as precise as the instrument that made it. If a ruler reads to the nearest millimeter, quoting a length as 12.3456 cm claims precision the ruler never had. Significant figures are a simple way to keep results honest: the answer of a calculation should not appear more precise than the data behind it. They are a rule of thumb rather than full error analysis; for careful lab work, uncertainties are propagated explicitly, but significant figures remain the standard for homework, lab reports and everyday reporting.

The calculator rounds half up: a following digit of 5 or more raises the last kept digit. Some labs use round half to even, also called banker's rounding, which sends 2.45 to 2.4 and 2.55 to 2.6 to avoid a slight upward bias over many roundings. The two methods differ only when the dropped part is exactly 5. Note too that computers store decimals in binary, so a value like 2.675 may be held as 2.67499999, which can affect the last digit of a rounded result in rare cases.

Writing a number as a coefficient times a power of ten puts every significant digit in the coefficient and nothing else. 1200 with two significant figures becomes 1.2 × 10³, with three becomes 1.20 × 10³, and with four becomes 1.200 × 10³. The power of ten carries only the size. That is why this tool switches to scientific notation whenever a plain answer would end in zeros that a reader could not interpret, and why journals and lab notebooks favor it for very large and very small measurements.