Significant Figures Calculator
Count the significant figures in any number, round to a target precision, or work out how many figures survive an addition, subtraction, multiplication, or division. Every result comes with a digit-by-digit visual so you can see exactly why each digit counts — or doesn't.
Background
Significant figures track how precisely a measurement is known. A ruler marked in millimeters can't honestly report a length to the nearest micron — sig fig rules keep calculated answers from claiming more precision than the original measurements actually have.
How to use this calculator
- Choose Count sig figs to see how many significant figures a number has, and why.
- Choose Round to reduce a number to a target number of significant figures, with proper rounding.
- Choose Arithmetic to see how many sig figs (or decimal places) survive a calculation between two measured numbers.
- Click Calculate to get a hero result, a color-coded digit visual, and a full step-by-step explanation.
The five rules of significant figures
All non-zero digits are always significant. In 482, that's all three digits.
Zeros trapped between non-zero digits are significant. In 4.008, both zeros count — there's no way to remove them without changing the value.
Leading zeros are never significant — they only place the decimal point. 0.0032 has just 2 sig figs; the leading zeros are placeholders.
Trailing zeros are significant only if the number has a decimal point. 2.50 has 3 sig figs, but plain 2500 is ambiguous — it could mean 2, 3, or 4 sig figs depending on how precisely it was measured.
In scientific notation, only the coefficient's digits count — the power of ten never adds or removes significance. 6.022×10²³ has 4 sig figs, same as 6.022 alone.
Formula & Equations Used
Rounding to N sig figs: find the digit N places after the first non-zero digit, then round using the usual "look at the next digit" rule — round-half-up on the digit that would follow.
Multiplication & division: sig figs(result) = min( sig figs(a), sig figs(b) ) — the least-precise measurement sets the ceiling for the whole calculation.
Addition & subtraction: decimal places(result) = min( decimals(a), decimals(b) ) — this uses decimal places, not sig fig counts, because you're lining up columns, not multiplying precisions.
Example Problems & Step-by-Step Solutions
Example 1 — Leading & trailing zeros
How many sig figs in 0.004500?
Step 1: The leading zeros (0.00) only mark the decimal position — not significant.
Step 2: Starting from the first non-zero digit (4), everything after it — 4, 5, 0, 0 — is significant, because the number has a decimal point.
Result: 4 significant figures.
Example 2 — Rounding
Round 3.14159 to 3 sig figs.
Step 1: The first 3 sig figs are 3, 1, 4.
Step 2: The next digit is 1, which rounds down.
Result: 3.14
Example 3 — Multiplication
4.56 (3 sig figs) × 1.4 (2 sig figs)
Step 1: Raw product = 6.384.
Step 2: The least precise input has 2 sig figs, so the result is capped at 2.
Result: 6.4 — not 6.384, even though that's mathematically exact.
Example 4 — Addition
18.0 (1 decimal place) + 1.013 (3 decimal places)
Step 1: Raw sum = 19.013.
Step 2: The least precise input has only 1 decimal place, so the result is rounded to 1 decimal place.
Result: 19.0
Frequently Asked Questions
Why do sig figs even matter?
A calculated answer can never be more precise than the least precise measurement that went into it. Reporting extra digits implies a precision the original measurements never had — sig fig rules keep answers honest about how well they're actually known.
Why is 1200 ambiguous but 1200. isn't?
Without a decimal point, there's no way to tell if the trailing zeros were measured or just placeholders. Adding an explicit decimal point (1200.) — or switching to scientific notation (1.200×10³) — removes the ambiguity and marks all four digits as significant.
Why do multiplication and addition use different rules?
Multiplication and division scale a value, so relative precision (sig figs) is what matters. Addition and subtraction just line up columns and add, so absolute precision (decimal places) is what matters — a number that's precise to whole units can't make a sum precise to hundredths, no matter how many sig figs it has.
Are exact numbers and constants affected?
Counted quantities (12 eggs) and defined constants (60 minutes per hour) are treated as having infinite sig figs — they never limit a calculation's precision. This calculator assumes every number you enter was measured, not counted or defined.
What rounding rule is used at exactly halfway?
This calculator rounds half away from zero (the common classroom convention): a digit of exactly 5 with nothing significant after it rounds the preceding digit up. Some labs use "round half to even" instead — check what your course or field expects.
Does scientific notation change how many sig figs a number has?
No — it just makes them unambiguous. 1200, 1.2×10³, and 1.200×10³ can all represent the "same" value, but they claim 2, 2, and 4 sig figs respectively. Scientific notation is the cleanest way to say precisely what you mean.
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