Significant Figures Calculator
Count the significant figures in a number, round to as many as you need, or combine two numbers and get the answer to the precision they actually support. In counting mode the digits that count are marked on the number itself, and every answer, in every mode, names the rule that produced it, so the working can be checked rather than trusted. The four counting rules and the two propagation rules are stated in full further down the page, because addition and multiplication do not follow the same one: multiplying keeps significant figures, adding keeps decimal places, and that difference is where most marks are lost.
0.004520 has 4 significant figures.
The counting rules. Every non-zero digit counts. Leading zeros only place the decimal point, so they never count. Trailing zeros past a decimal point are measured digits, so they count: nobody writes them by accident.
Worked cases
Each one is computed by the same code that answers your own numbers, every time this page loads.
The rules
Four rules decide which digits count, and two more decide what survives an operation. The example under each rule is computed by the calculator above, not written out here.
Every non-zero digit counts
1 through 9 are always significant, wherever they sit in the number. This is the rule the other three qualify, and on a number with no zeros in it, it is the only rule you need.
4521 → 4 significant figures
Zeros between non-zero digits count
A zero with a counted digit on each side was measured like any other digit, so it counts. Position makes no difference: a captive zero counts whether or not there is a decimal point anywhere in the number.
1004 → 4 significant figures
Leading zeros never count
Zeros in front of the first non-zero digit only place the decimal point, so they carry no measurement. 0.00452 and 4.52 claim exactly the same three figures, which is why the count does not change when you switch from metres to millimetres.
0.00452 → 3 significant figures
Trailing zeros count past a decimal point
A zero written after the last non-zero digit, with a decimal point in the number, is a measured digit: nobody writes it by accident. Without a decimal point it is genuinely ambiguous, and 1200 is read as 2 figures by the convention. Write 1200. or 1.200 × 10³ when you mean 4.
1.200 → 4 significant figures
Multiplication and division keep significant figures
The answer carries as many significant figures as the input with the fewest. 12.5 has three and 3.2 has two, so the product is given to two, and the extra digits your calculator shows are not knowledge you had.
12.5 × 3.2 → 40
Addition and subtraction keep decimal places
Here it is decimal places, not figures, that carry: the answer is only as precise as the coarsest input. 12.52 is good to two places and 3.1 to one, so the sum is given to one place. Notice that the answer keeps three significant figures, more than 3.1 had, which is exactly why the two rules cannot be swapped.
12.52 + 3.1 → 15.6
Common questions
- What are the rules for counting significant figures?
- Four of them. Every non-zero digit counts. Zeros between non-zero digits count. Leading zeros never count, because they only place the decimal point, so 0.00452 and 4.52 both claim three figures. Trailing zeros count when a decimal point is written: 1.200 claims four. All four are stated in full on this page with a worked example under each, and every example is computed by the calculator above rather than typed in, so an example here cannot disagree with the answer you get.
- Do trailing zeros count as significant figures?
- Past a decimal point, yes: nobody writes 1.200 by accident, so all four digits count. In a whole number with no decimal point it is genuinely ambiguous, and 1200 might mean two figures or four. The convention reads it as two, and this page gives that reading, flags it, and shows the other reading beside it rather than choosing silently. Write 1200. or 1.200 × 10³ when you mean four.
- Why do addition and multiplication use different rules?
- Because they lose precision in different ways. Multiplication and division keep significant figures: 12.5 × 3.2 is 40, two figures, because 3.2 only had two. Addition and subtraction keep decimal places: 12.52 + 3.1 is 15.6, one decimal place, because 3.1 was only measured to one. Notice that the sum keeps three significant figures, more than 3.1 carried, which is exactly why one rule cannot stand in for the other. This page applies them separately and names which one it used on every answer.
- How do I write an ambiguous number so the count is clear?
- Two ways. Put a decimal point at the end, so 1200. says all four digits were measured. Or use scientific notation, where the mantissa carries exactly the figures you claim: 1.2 × 10³ says two, 1.200 × 10³ says four. This page prints the second form whenever a plain answer would understate the count, and it accepts either form typed back in, along with E notation such as 1.20e3.
- Does this round the way my course expects?
- It rounds half away from zero: when the digit after the last kept one is 5 or more, the kept digit goes up. That is the rule most chemistry and physics courses teach. Some courses and some languages use round half to even instead, which sends 2.5 to 2 rather than 3. If yours does, the rounding calculator on this site shows the same number under ten different rounding rules side by side. One thing this page does not do is round the binary approximation of your number: 1.005 to three figures is 1.01 here, where a calculator working in floating point answers 1.00.
- Is anything uploaded?
- No. The counting and the arithmetic happen in this page, in your browser, so no number you type leaves the machine you typed it on. There is no account, no upload and no limit on how many numbers you run through it.
Exact. Counting and rounding to significant figures is a stated convention applied literally, and the page shows which digits it counted and which rule it used. Where a trailing zero is genuinely ambiguous without a decimal point, it says so rather than choosing for you.