Significant Figures Calculator
Count significant figures in any number, including decimals, scientific notation, and numbers with leading or trailing zeros. See which digits count and why.
1.20e3 or 1.20E3).
How the significant figures calculator works
Significant figures (sig figs) are the digits in a measurement that carry real precision. Placeholder zeros that only serve to locate the decimal point do not count. This tool parses the number you enter, walks each digit, and applies the five standard rules to decide which digits are significant and which are merely placeholders.
The five rules
- All non-zero digits are significant. 1, 2, 3, 4, 5, 6, 7, 8, 9 always count. In 347, all three digits are significant.
- Zeros between non-zero digits are significant. These are "captive" zeros. In 1002, all four digits — including both zeros — count.
- Leading zeros are not significant. They only position the decimal point. In 0.00450, the three zeros before the 4 are not significant. Sig figs = 3 (the 4, 5, and trailing 0).
- Trailing zeros in a decimal number are significant. Writing 12.300 rather than 12.3 is a deliberate statement of precision. 12.300 has five sig figs.
- Trailing zeros in a whole number without a decimal point are ambiguous. 12000 could mean anywhere from two to five sig figs. The honest fix is scientific notation: 1.2 × 10⁴ (two sig figs) or 1.2000 × 10⁴ (five).
Worked examples
0.004500 — The three leading zeros are placeholders. The 4 and 5 are significant, and so are the two trailing zeros (they are after the decimal). Count: 4 sig figs.
1.20 × 10³ — In scientific notation, every digit in the coefficient is significant. The 1, 2, and 0 all count. Count: 3 sig figs.
1002 — All four digits are significant; the interior zeros are captive. Count: 4 sig figs.
12000 — Ambiguous. Could be anywhere from 2 to 5 sig figs. The calculator flags this and reports the maximum plausible count (5). To be unambiguous, write 1.2 × 10⁴, 1.20 × 10⁴, 1.200 × 10⁴, or 1.2000 × 10⁴.
Edge cases and gotchas
Pure zero. The number 0 is a special case — conventions vary, but most textbooks treat it as undefined for sig figs since there is no measurement precision encoded. If you enter 0, the tool returns a non-positive result.
Exact numbers. Counts of discrete objects (12 students) and defined constants (exactly 100 cm in a metre) have infinite significant figures. Sig-fig rules apply to measurements, not counts.
Scientific notation with negative exponents. 6.02 × 10⁻⁴ has three sig figs. The sign of the exponent does not affect the count — only the coefficient matters.
Bar-notation for ambiguous trailing zeros. Some textbooks draw a bar over the last significant zero (e.g., 1200̄ for three sig figs). We do not parse this notation — use scientific notation instead, which is universal.
Why sig figs matter
Significant figures communicate measurement uncertainty. Reporting a temperature as 23.456 °C implies you measured to the thousandths place; reporting it as 23 °C implies only unit precision. Using the wrong number of sig figs in a lab report overstates or understates the reliability of the data. In arithmetic, the result should not be more precise than the least-precise input: multiplying 2.5 (two sig figs) by 3.14159 (six sig figs) should yield 7.9, not 7.854.
What this calculator is not
This tool counts sig figs in a single number. It does not perform sig-fig-aware arithmetic — for that, you would round each intermediate to the appropriate precision based on the operation (multiplication/division uses the least sig-fig input; addition/subtraction uses the least decimal-place input). It also does not handle bar-notation or uncertainty ranges like 12.3(4). For those, write the number in explicit scientific notation first.