Significant Figures Calculator
Count significant figures, round a number to 1 through 20 figures, or combine two measured numbers with +, −, × or ÷. Count marks the digits it uses; Round to keeps requested trailing zeros and uses scientific notation when an integer would hide the figure count. Operate applies decimal places to addition and subtraction, and significant figures to multiplication and division. Each answer explains its rule and shows the exact arithmetic result before measurement rounding. Decimal numbers and scientific notation are accepted, including 1.20e3 and 1.20 × 10³.
0.004520 has 4 significant figures.
- Number
- Mode
Use a decimal point. Each number accepts up to 200 characters and exponents from -1000 to 1000. Rounding, multiplication and division display at most 20 significant figures. Longer pasted drafts stay visible for repair.
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?
- This page uses half away from zero: when the first discarded digit is 5 or more, the result rounds away from zero. For example, 1.005 to three figures is 1.01 and -1.005 becomes -1.01. Some courses use half to even instead. The separate rounding calculator offers that choice and nine other rules. The number here is rounded from its decimal digits, with no binary floating-point conversion in the rounding decision.
- How do I round to one, two, three, four or five significant figures?
- Choose Round to, enter the number and set Figures to the requested count. Start at the first non-zero digit, retain that many digits and inspect the next digit. 25446 to one figure is 3 × 10⁴, 0.725 to two is 0.73, 1.005 to three is 1.01, 12.345 to four is 12.35 and 12.3456 to five is 12.346. The worked cases above load these jobs into the calculator.
- Why does 2.009 rounded to two significant figures become 2.0?
- The kept digits are 2 and the next zero. The following digit is 0, so the last kept digit does not increase. Writing 2.0 preserves two figures; writing only 2 would claim one. Likewise, 4382 to one figure is 4 × 10³, or 4000 understood as one figure, and 0.36 to one is 0.4.
- What is the difference between decimal places and significant figures?
- Decimal places count digits after the decimal point. Significant figures start at the first non-zero digit and include measured trailing zeros. For 0.004520 the calculator reports six decimal places and four significant figures. Round to selects figures; it does not select decimal places. Use the rounding calculator for a chosen decimal-place target. Operate automatically uses the coarsest decimal place for addition and subtraction.
- Can I count and round significant figures in scientific notation?
- Yes. Count reads the written coefficient, so 1.200e3 has four figures; the exponent does not count. Round to accepts E notation and × 10 with a signed exponent or superscripts. To write a rounded result with an unambiguous count, use the Without the ambiguity output when it appears in Operate. Rounding 1204 to three figures gives 1.20 × 10³. This page also prints scientific notation for exact arithmetic results whose plain decimal is long.
- How do multiplication, division and density use significant figures?
- Choose Operate and × or ÷, then enter two measured numbers. The result keeps the smaller input figure count, with a 20-figure display cap. For example, 12.5 × 3.2 gives 40, stated unambiguously as 4.0 × 10¹, and 100.0 ÷ 3.00 gives 33.3. For a supplied density calculation, divide the mass coefficient by the volume coefficient after putting the values in compatible units yourself: 12.50 g ÷ 2.0 mL gives 6.3 g/mL. Enter 12.50 and 2.0; the calculator does not parse unit labels, convert units or solve a density model.
- Can I use this for chemistry or physics measurements?
- Yes, for counting written measurement digits, rounding a supplied numeric value and applying the displayed two-input arithmetic conventions. Leading zeros place the decimal point; written trailing zeros state precision. The tool cannot infer the precision of an instrument or whether a number is an exact constant. It treats both operands as measured, so counts, defined conversion factors and exact constants can need a different precision decision. Supply the numeric coefficients yourself and keep their units outside the input fields.
- Does this calculate equations, uncertainty, error bounds, logs or standard deviation?
- No. Operate performs one selected operation on two numbers. It does not parse a whole expression, propagate uncertainty, calculate upper and lower measurement bounds, evaluate logarithms or square roots, or calculate standard deviation with a significant-figure propagation rule. Rounding a result you computed elsewhere does not complete those jobs here. It also reads one number at a time rather than a pasted batch.
- What number formats and limits are accepted?
- Use a decimal point, an optional sign and optional scientific notation. Integer digits can be grouped in threes with one consistent comma, space, underscore or apostrophe separator, such as 1,234.50. Decimal commas such as 1,5, malformed groups, unit labels, fractions and separators in a fraction or exponent are rejected. Each input accepts up to 200 characters and exponents from -1000 to 1000. Longer drafts stay visible for correction. Rounding, multiplication and division output up to 20 figures; the rule explains when that cap is below the input precision. Addition and subtraction follow the stated decimal places.
- What is the exact arithmetic result shown below an answer?
- It is the arithmetic value before the measurement precision rule is applied. Addition, subtraction and multiplication show an exact decimal value, or an exact scientific form when the plain decimal is long. Division shows an exact terminating decimal when possible and an exact reduced fraction for a repeating quotient, such as 100/3. It avoids the underflow, overflow and shortened digits of a floating-point preview. The rounded answer and its precision rule are shown separately.
- Will this change my scientific calculator settings or install an app?
- No. It runs in this browser. Use Count, Round to or Operate here; it does not configure a TI-84, Casio or another device, and it is not a downloadable native calculator app.
- 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. Counts written digits and applies half-away-from-zero rounding with decimal integer arithmetic. Rounding, multiplication and division output at most 20 significant figures; addition and subtraction follow decimal places. Each input accepts up to 200 characters and exponents from -1000 to 1000. Ambiguous integer zeros are flagged, and the arithmetic result before measurement rounding is shown exactly.