Significant Figures Calculator
See exactly which digits count and why, round to any number of sig figs, and do lab math with the right precision.
By Manzoor Ahmad, pharmacist · Updated How do you count significant figures?
Count every non-zero digit, every zero between them, and trailing zeros only when there is a decimal point; leading zeros never count. 0.004050 has 4 significant figures (4, 0, 5, 0). 1200 is ambiguous (2 to 4), while 1200. has 4 and 1.20 × 10³ has 3.
Significant figure rules with examples
| Rule | Example | Sig figs |
|---|---|---|
| Non-zero digits always count | 4.37 | 3 |
| Zeros between non-zero digits count | 305.2 | 4 |
| Leading zeros never count | 0.0025 | 2 |
| Trailing zeros after a decimal point count | 2.500 | 4 |
| Trailing zeros with no decimal point are ambiguous | 1200 | 2 to 4 |
| A decimal point makes trailing zeros count | 1200. | 4 |
| Scientific notation shows them clearly | 1.20 × 10³ | 3 |
| Exact and counted numbers are unlimited | 12 eggs, 1 in = 2.54 cm | ∞ |
Rules for calculations
- Multiply or divide: keep the fewest significant figures. 2.5 × 3.42 = 8.55 → 8.6.
- Add or subtract: keep the fewest decimal places. 12.11 + 18.0 = 30.11 → 30.1.
- Mixed steps: carry extra digits through the working and round once at the end.
- Logarithms: the number of decimal places in a log equals the sig figs in the original value, which is why a pH of 4.70 comes from [H⁺] = 2.0 × 10⁻⁵ (see the pH calculator).
Significant figures FAQs
Significant figures (sig figs) are the digits in a measured number that carry meaning about its precision: all non-zero digits, zeros between them, and trailing zeros when a decimal point is shown.
Four. The leading zeros (0.00) are placeholders, 4 and 5 are non-zero, the zero between them is trapped and counts, and the final zero after the decimal point counts.
Only if the number has a decimal point. 1200. and 1200.0 have 4 and 5 sig figs, but 1200 is ambiguous: it could have 2, 3 or 4. Write it in scientific notation, such as 1.20 × 10³, to remove the doubt.
No. Zeros before the first non-zero digit only locate the decimal point. 0.0025 has two significant figures.
Count from the first non-zero digit to the required number of digits, then look at the next digit: 5 or more rounds up, less than 5 leaves it. 0.0123456 to 3 sig figs is 0.0123; 9.996 to 3 sig figs is 10.0.
The answer keeps as many significant figures as the measurement with the fewest. 2.5 × 3.42 = 8.55, which rounds to 8.6 (two sig figs, limited by 2.5).
The answer keeps as many decimal places as the measurement with the fewest. 12.11 + 18.0 = 30.11, which rounds to 30.1 (one decimal place, limited by 18.0).
No. Counted values (3 tablets) and defined constants (1 inch = 2.54 cm, 1000 mL in 1 L) have unlimited sig figs and never limit the answer.
Keep at least one or two extra digits through intermediate steps and round only the final answer. Rounding early can shift the last digit.
Also called banker's rounding: a 5 followed by nothing rounds to the nearest even digit, so 2.5 → 2 and 3.5 → 4. It avoids a slight upward bias and is used by some labs and standards.
It depends on how it was measured. 0.00 g on a two-decimal balance is usually treated as having its decimal places as the precision; this calculator reports the digits after the decimal point.
Writing 5.0 mg can be misread as 50 mg if the decimal is missed, so the Institute for Safe Medication Practices advises against trailing zeros in medication orders (write 5 mg) and always using a leading zero (0.5 mg, not .5 mg). Precision rules in the lab and safety rules on a prescription work hand in hand.
Sources
- NIST: Guide for the Use of the International System of Units (SP 811), rounding and significant digits
- OpenStax Chemistry 2e, Section 1.5: Measurement Uncertainty, Accuracy, and Precision
- Institute for Safe Medication Practices: List of Error-Prone Abbreviations, Symbols and Dose Designations
- NIST Technical Note 1297: Guidelines for Evaluating and Expressing the Uncertainty of Measurement Results
- IEEE 754: Standard for Floating-Point Arithmetic (rounding modes)
Sig fig rules are a convention for showing precision. For formal work, report a measured value with its stated uncertainty, as NIST recommends.