Clever Quest Lab Tools

Significant Figures Calculator

2026-10-06

Count the significant figures in any number, round it to 1–30 significant figures, or add, subtract, multiply and divide measurements with the correct sig fig rules. Results update as you type and show every step.

Count significant figures

Plain (0.00450, 1500., -0.0305) or scientific (6.022e23, 1.20E-3, 1.20 x 10^3).

Round to n significant figures

Rounding rule: round half up (half away from zero). If the first dropped digit is 5 or more, the last kept digit goes up.

Calculate with sig fig rules

Calculations run in your browser; nothing you type is sent anywhere.

Every number you type is treated as a measured value. Exact numbers, such as a count of 12 eggs or a defined factor like 100 cm = 1 m, have unlimited significant figures and should not limit the rounding of your answer. Rounding is done only at the end, on the exact result.

How to use the significant figures calculator

  1. To count, type a number into the first card. Plain decimals (0.00450, 1500., -0.0305) and scientific notation (6.022e23, 1.20 x 10^3) both work. The significant digits are shown bold and underlined, the others dimmed.
  2. To round, enter a number and a target between 1 and 30 significant figures in the second card. You get the plain and the scientific form.
  3. To calculate, enter two numbers and pick +, −, × or ÷. The tool shows the exact result, the rule it applied and the correctly rounded answer.
  4. Use Copy to paste a result into your lab report, and Reset to return to the examples. Your entries are remembered in this browser.

How it works

The tool never converts your input to a floating-point number. It reads the digits you typed and a power of ten, and does all arithmetic on whole numbers. That is why 1.0 keeps its zero, 2.675 is exactly 2.675 and 0.1 + 0.2 is exactly 0.3.

The counting rules are:

To round to n significant figures, keep the first n digits starting at the first non-zero digit and look at the next one. If it is 5 or more, the last kept digit goes up by one (round half up, away from zero); otherwise it stays. Some courses use round-half-to-even instead, where an exact 5 rounds to the nearest even digit. Check which one your instructor expects.

For calculations the tool applies one of two rules to the exact result:

add or subtract: round to the least precise decimal place
multiply or divide: keep min(sf(A), sf(B)) significant figures

Here sf(A) is the number of significant figures of operand A. The least precise decimal place is the place of the last significant digit, taking the coarsest one among the operands. Additions, subtractions and multiplications are exact; divisions are carried to at least 40 digits before rounding.

Examples

Counting. 0.00450 has 3 significant figures: the three leading zeros do not count, the final zero does. 1500 has 2 (the tool treats the two trailing zeros as placeholders), 1500. has 4, and 1.50 x 10^3 has 3.

Rounding. Round 2.675 to 3 significant figures: keep 2.67, the next digit is 5, so the answer is 2.68. Many calculators and programming languages show 2.67, because 2.675 is stored in binary as a value slightly below 2.675. 9.995 to 3 figures is 10.0: the carry moves the decimal point, and the zero is kept so the answer still shows three figures.

Adding. 12.11 + 18.0 = 30.11. The 18.0 is only known to tenths, so the answer is rounded to one decimal place: 30.1. In 1200 + 34.5 = 1234.5, the 1200 is known only to the hundreds place, so the answer is 1200, written 1.2 x 10^3 in scientific notation.

Multiplying and dividing. 4.56 × 1.4 = 6.384. The 1.4 has 2 significant figures, so the answer is 6.4. 10.0 ÷ 3.0 is 3.3333… and also becomes 3.3.

Why addition and multiplication use different rules

When you add or subtract, the uncertainties add in absolute terms: if one value is only good to the nearest 0.1, the sum cannot be better than 0.1, however many digits the other value has. That is why the rule looks at decimal places. When you multiply or divide, it is the relative uncertainty (the uncertainty as a fraction of the value) that carries through, and the number of significant figures is a rough measure of that fraction. So the rule counts figures, not places.

Mixing the rules is the most common mistake. 100.0 − 0.55 = 99.45 becomes 99.5 (one decimal place, from 100.0), even though 0.55 has only two significant figures. 2.5 × 3.42 = 8.55 becomes 8.6 (two significant figures, from 2.5).

Exact numbers and guard digits

Counted items (12 eggs) and defined conversion factors (1 inch = 2.54 cm exactly) have unlimited significant figures, so they never limit the answer. The calculator cannot know which numbers are exact: it treats everything you type as measured. If one operand is exact, ignore it when deciding how many figures the answer should have, or type it with plenty of digits.

In a calculation with several steps, do not round after every step. Keep one or two extra “guard digits” in the intermediate results and round only the final answer. Rounding early adds rounding errors that can change the last digit of the result. This tool does exactly that within a single operation: it rounds the exact result once.

Scientific notation removes the ambiguity

The number 1500 could have been measured to the nearest 1, 10 or 100. Scientific notation settles it, because every digit in the mantissa counts: 1.5 x 10^3 has 2 significant figures, 1.50 x 10^3 has 3 and 1.500 x 10^3 has 4. The same applies to results. Rounding 1500 to 3 figures gives 1500 in plain notation, which looks like it has 2, so the tool also shows 1.50 x 10^3. Use that form in reports whenever a whole number ends in zeros. For very large and very small values, such as 6.022 x 10^23, it is also the natural way to write them.

Frequently asked questions

Why does 1500 have only 2 significant figures here?

Without a decimal point, the trailing zeros of a whole number are ambiguous. The tool uses the common textbook choice of counting them as not significant. Write 1500. or 1.500 x 10^3 to show 4 figures.

Is zero significant?

A zero is significant when it sits between non-zero digits or after the decimal point at the end of a number. The number 0 on its own has no non-zero digit; the tool reports 1 as a convention.

Does the calculator round half up or half to even?

Half up: a first dropped digit of 5 or more rounds the last kept digit up, away from zero. Some courses prefer round-half-to-even, which only differs when the dropped part is exactly 5.

How many significant figures should my final answer have?

For addition and subtraction, round to the least precise decimal place of the inputs. For multiplication and division, use the fewest significant figures of the inputs. In longer calculations, apply each rule to its own step, but only round at the end.

What input formats are accepted?

Plain decimals with an optional sign and leading zeros, such as 007.50 or +12.0, and scientific notation written as 6.022e23, 1.20E-3, 1.20 x 10^3, 1.20×10^3 or 1.20*10^-3. Thousands separators are not accepted.

Is my data sent anywhere?

No. All calculations run in your browser and nothing is uploaded. Your last entries are stored only in this browser, in local storage, so they are still there when you return.

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