Uncertainty & measurement
Significant Figures Calculator
Round the number as written, including scientific notation. The output keeps significant trailing zeros explicit.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
Calculated locally. No account or uploads.
Result & working
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Step-by-step working
The formula
Keep N significant digits; round up if the first discarded digit is 5–9.
| Symbol | Meaning |
|---|---|
| N | Requested number of significant figures, from 1 to 15. |
| e notation | 1.20e-3 means 1.20 × 10⁻³. The exponent does not change the significant-figure count. |
When to use this calculator
Use significant figures to report a result to an appropriate precision. Leading zeros locate the decimal point: 0.004520 has four significant figures. The zero between 1 and 2 in 1.02 is significant.
Trailing zeros in 1200 are ambiguous without more context. Write 1.2 × 10³ for two significant figures or 1.200 × 10³ for four. This calculator rounds decimal strings directly, so an exact decimal tie such as 1.005 to three significant figures becomes 1.01.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- Input: 0.004520
- Requested significant figures: 3
- Rounded scientific notation: 4.52 × 10^-3
- The written input indicates 4 significant figures. Leading zeros are not significant; zeros between significant digits are significant. Trailing zeros in a decimal or scientific-notation mantissa express precision. The first discarded digit determines rounding. Exact halfway cases round away from zero. Adding zeros cannot improve measurement precision.
4.52 × 10^-3
Common mistakes
- Significant figures and decimal places are different.
- Adding trailing zeros does not create more accurate measurements.
- Keep unrounded values during intermediate calculations.
- A measured zero needs resolution or an absolute uncertainty to communicate precision.