Significant Figures Calculator
Count significant figures, round to N sig figs, and perform arithmetic preserving correct sig figs for chemistry, physics, and engineering.
MATHCount significant figures in any number, round to a specific number of sig figs, and perform arithmetic (+ - Γ Γ·) preserving the correct sig figs. Built for chemistry, physics, and engineering students who need to report results with appropriate measurement precision.
Sig fig rules: (1) all non-zero digits are significant; (2) zeros between non-zero digits are significant; (3) leading zeros are NOT significant; (4) trailing zeros after a decimal point ARE significant; (5) trailing zeros in whole numbers are ambiguous - use scientific notation to disambiguate. For multiplication/division, the result has the fewest sig figs of any input. For addition/subtraction, the result has the fewest decimal places of any input. Keep extra digits during intermediate steps and round only at the end.
Significant Figures Calculator (Sig Fig Counter & Rounder)
Count significant figures in any number, round to a specific number of sig figs, or perform arithmetic (+ β Γ Γ·) preserving the correct sig figs. Built for chemistry, physics, and engineering students.
Sig Fig Rules
- All non-zero digits are significant (123 has 3 SF).
- Zeros between non-zero digits are significant (102 has 3 SF).
- Leading zeros are NOT significant (0.0052 has 2 SF).
- Trailing zeros after a decimal ARE significant (5.00 has 3 SF).
- Trailing zeros in a whole number are ambiguous (100 has 1, 2, or 3 SF - use scientific notation to disambiguate).
How Significant Figures Work
Significant figures (sig figs) communicate measurement precision. The rule: a result of a calculation cannot be more precise than the least precise input. If you measure a length as 5.2 cm (2 SF) and another as 3.456 cm (4 SF), the sum should be reported as 8.7 cm (NOT 8.656 cm) - addition follows decimal-places-based rules and the least-precise input has 1 decimal place.
For multiplication and division, the result has the same number of sig figs as the input with the fewest sig figs. 5.2 Γ 3.456 = 17.9712 raw, but reported as 18 (2 SF, matching 5.2). For addition and subtraction, the result has the same number of decimal places as the input with the fewest decimal places. 5.2 + 3.456 = 8.656 raw, reported as 8.7 (one decimal place).
Common pitfalls: (1) Mixing sig figs at every step accumulates rounding error - keep extra digits during intermediate calculations and round only the final result. (2) Whole numbers like "5 apples" are exact, not measured - they do not limit sig figs. (3) Constants from physics (Ο, e, c) carry effectively infinite sig figs. (4) Use scientific notation (5.20 Γ 10Β²) to clearly indicate sig figs in numbers ending in zeros.
Sig fig rules are conventions, not laws. Different disciplines (chemistry vs engineering) sometimes apply different conventions. Always follow your instructor or workplace standard.