Significant Figures Calculator
Significant figures
3
How it works
Significant figures (sig figs) express the precision of a measurement — they indicate which digits are meaningfully known. In scientific calculations, the result can only be as precise as the least precise measurement that contributed to it. The Significant Figures Calculator rounds any number to a specified number of significant figures and identifies sig figs in existing values.
**Rules for counting sig figs** 1. All non-zero digits are significant: 1234 has 4 sig figs. 2. Zeros between non-zero digits are significant: 1002 has 4 sig figs. 3. Leading zeros are NOT significant: 0.0034 has 2 sig figs (3 and 4). 4. Trailing zeros AFTER a decimal point are significant: 2.300 has 4 sig figs. 5. Trailing zeros WITHOUT a decimal point are ambiguous: 1200 could have 2, 3, or 4 sig figs — use scientific notation to be explicit (1.2 × 10³ = 2 sig figs; 1.200 × 10³ = 4 sig figs).
**Multiplication and division** Result has the same number of sig figs as the measurement with the fewest: 4.53 × 2.1 = 9.513 → round to 2 sig figs = 9.5 (because 2.1 has only 2 sig figs).
**Addition and subtraction** Result is rounded to the same decimal place as the measurement with the fewest decimal places: 12.52 + 0.8 = 13.32 → round to 1 decimal place = 13.3 (because 0.8 has only 1 decimal place).
**Why this matters in labs** Reporting 9.51300 when a thermometer reads to 0.1°C precision implies false accuracy. The calculator enforces correct sig fig reporting for lab data, physics problem sets, and chemistry calculations — and shows step-by-step rounding work.
Privacy: all calculations run in the browser. No data is transmitted.
Frequently Asked Questions
- Write it in scientific notation: 1.20 × 10³. The trailing zero after the decimal point is now explicitly significant (rule: trailing zeros after a decimal ARE significant). Alternatively, place a decimal point after the last significant digit with an underline (1200.) to indicate 4 sig figs, or write 1.200 × 10³ for 4 sig figs. For 3 sig figs specifically: 1.20 × 10³. This ambiguity in trailing zeros without a decimal is why scientific notation is essential in laboratory reporting — it removes all ambiguity about which digits are significant.
- No — exact numbers (defined quantities, not measurements) have infinite significant figures and don't limit your answer's precision. Examples of exact numbers: 1 inch = 2.54 cm exactly (by definition, not measurement); 1 dozen = 12 exactly; the number of sides on a square = 4. When you calculate the circumference of a circle (C = 2πr), the 2 is exact, π is mathematically exact (not limited by sig figs), and only the measured radius r limits precision. The count of 5 students in a class is exact — you wouldn't round it.
- Multiplication/division: the relative uncertainty of the result equals the combined relative uncertainties of the inputs. Relative uncertainty ≈ 1/sig_figs. To prevent error accumulation, the result's relative uncertainty can't be smaller than the largest input relative uncertainty — hence: same number of sig figs as the least precise input. Addition/subtraction: the absolute uncertainty of the result equals the combined absolute uncertainties. The result can't be more precise than the least precise decimal place — hence: same decimal place as the least precise input. These are the propagation-of-uncertainty rules simplified for lab work.
- Use the same number of sig figs as your least precise measurement (for multiplication/division results) or the same decimal place as your least precise measurement (for addition/subtraction results). For final reported values: one or two extra digits in intermediate calculations to avoid rounding errors accumulating. Report uncertainties alongside values: 9.5 ± 0.1 cm explicitly states both the measurement and its precision. When in doubt, use 3 significant figures — it's rarely wrong for a student lab context and matches most instruments (digital scales, rulers, thermometers).