163
Count and round significant figures
On the default, 0.0045070 → 5 sig figs, rounded to 3 sig figs → 0.00451. Enter your own number below.
FREE TOOL · MATH
Significant Figures Calculator
Type any number and see exactly how many significant figures it carries — and what it becomes rounded to your target. The five counting rules, the ambiguous trailing zeros, and the toPrecision form, all shown on the default below.
The five counting rules, with examples
| Rule | Example | Sig figs |
|---|---|---|
| All non-zero digits count | 421.7 | 4 |
| Leading zeros never count | 0.0045070 | 5 (the 4, 5, 0, 7, 0) |
| Zeros between non-zero digits count | 1,001 | 4 |
| Trailing zeros count with a decimal point | 1.200 | 4 |
| Trailing zeros are ambiguous without one | 1,200 | 2, 3, or 4 — unknowable |
Why the ambiguity matters: 1,200 could mean a rough estimate (2 sig figs), a measurement to the tens place (3), or an exact-to-ones count (4) — the digits alone cannot tell you. Scientists write 1.20×10³ (3 sig figs) or 1.200×10³ (4) to kill the ambiguity. The calculator flags any bare number ending in zero so you see the trap.
Output · formula · meaning
| Output | Formula | What it means |
|---|---|---|
| Significant-figure count | strip sign, leading zeros; count the rest | 0.0045070 → 5; 1200 → flagged ambiguous. |
| Rounded to N sig figs | x.toPrecision(N) | 0.0045070 to 3 sig figs → 0.00451. |
| toPrecision form | the exact rounded string | useful when 4.5 and 4.50 differ — they do here. |
The rounding rule: exactly 5 rounds up
Dropping digits is normal rounding with one sharp edge: a dropped portion of exactly 5 followed by nothing rounds up — 4.5 to 1 sig fig becomes 5, and 0.0045 to 2 sig figs becomes 0.0045 → wait, 0.0045 already has 2. A cleaner case: 2.449 to 2 sig figs → 2.4 (dropped 0.049 < 0.05), 2.451 → 2.5. Some textbooks teach "banker's rounding" (5 to even); this calculator uses the standard round-half-up most school courses expect.
Exact numbers have infinite sig figs
Counted quantities — 24 hours in a day, 100 people surveyed, 2 sides of a coin — are exact. They never limit your answer: if you average 100 exact measurements, the divisor 100 does not cap the result at 3 sig figs. Only measured numbers bring limited precision; definitions (1 inch = 2.54 cm exactly) do too.
Who uses this
- Chemistry & physics students: every lab report gets graded on sig figs — this is where the marks live.
- Engineers & machinists: a dimension quoted as 25.00 mm promises ten times the precision of 25 mm.
- Data analysts: stopping a dashboard at 3 sig figs instead of the calculator's 12 digits.
- Anyone citing measurements: 4.50 g and 4.5 g are different claims — the trailing zero is a promise.
Accuracy & limitations
Counting follows the standard five rules; rounding uses round-half-up to N sig figs via exact decimal string formatting (no floating-point drift in the displayed answer). Bare trailing zeros (1200) are flagged as ambiguous rather than guessed. Exact counted numbers are treated as infinite-precision inputs — if your "24" is measured, not counted, the verdict's infinite-precision note does not apply.
Converting between forms too? The decimal to fraction converter keeps exactness, the fraction simplifier cleans up the result, and the binary, hex & decimal chart covers base conversions.
Cite this calculatorBright Side Kit. “Significant Figures Calculator & Rounder.” brightoolbox.com, 2026.
Bright Side Kit. "Significant Figures Calculator & Rounder." https://brightoolbox.com/significant-figures-calculator/ Accessed October 22, 2026.Frequently asked questions
How many significant figures does 0.0045070 have?
5 — the 4, 5, 0, 7, and 0. Leading zeros never count; every digit from the first non-zero one on does, because the number has a decimal point.
Are trailing zeros significant in 1200?
It is ambiguous. 1,200 could carry 2, 3, or 4 sig figs — the digits alone cannot say. Writing 1.200×10³ pins it to 4; 1.2×10³ pins it to 2. With a decimal point (1200.), trailing zeros always count.
Why do scientists bother with significant figures?
Because digits are claims about precision. Writing 4.50 g says you measured to the hundredth; writing 4.5 g says only the tenth. Dropping the zero understates your work; adding one invents precision you never had.
What is the rule for rounding a 5?
Standard school rule: round half up. 2.5 → 3, 2.451 to 2 sig figs → 2.5. (Some statistics courses teach banker's rounding — 5 to the nearest even digit — so check your syllabus.)
Do exact numbers count toward significant figures?
No — they have infinite sig figs. Counted items (100 people, 24 hours) and exact definitions (1 in = 2.54 cm) never limit a result. Only measurements do.
How many sig figs should my answer have?
For multiplication and division: as many as the least-precise input. For addition and subtraction: match the decimal place of the least-precise input, not the digit count. Keep extra digits mid-calculation and round once at the end.
What is the difference between 4.5 and 4.50?
One significant figure of meaning. 4.50 promises the second digit — it says "forty-five hundredths, and the next digit is zero." That is why the calculator shows the toPrecision form: it preserves the promise.