Significant Figures Calculator
Count significant figures in any number and round to a specified number of sig figs. Covers all sig fig rules with explanations. Extended: operations with proper sig fig treatment. Professional: error propagation and uncertainty analysis.
Quick Calculator Get a fast estimate
Significant Figures
5
Integer without decimal point
Digits (no leading zeros): "12300"
Note: 2 trailing zero(s) — ambiguous without decimal point
Minimum sig figs: 3, Maximum: 5
How to Use the Significant Figures Calculator
Enter any number to count its significant figures. Switch to Round mode and enter a target number of sig figs to round. The calculator explains which digits count and why.
The Extended Calculator covers sig fig rules for arithmetic operations. The Professional Calculator propagates measurement errors through calculations.
Need more detail?
Extended Calculator More options, charts, and scenario comparison
Rounded to 2 significant figures
0.0041
Original
0.004050
Scientific notation
4.1e-3
Significant Figures Rules
1. Non-zero digits are ALWAYS significant
Example: 456 → 3 sig figs
2. Zeros between non-zeros are SIGNIFICANT
Example: 4006 → 4 sig figs
3. Leading zeros are NEVER significant
Example: 0.0045 → 2 sig figs
4. Trailing zeros WITH decimal: SIGNIFICANT
Example: 4.500 → 4 sig figs
5. Trailing zeros WITHOUT decimal: ambiguous
Example: 4500 → 2 to 4 sig figs (use 4.50×10³ for clarity)
Sig Fig Rules for Calculations
| Operation | Rule | Example |
|---|---|---|
| Add/Subtract | Fewest decimal places | 12.5 + 1.23 = 13.7 |
| Multiply/Divide | Fewest sig figs | 3.4 × 2.56 = 8.7 |
| Exact numbers | Unlimited sig figs | 2πr (2 is exact) |
Need full precision?
Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown
Value a ± δa
Value b ± δb
Result z ± δz
14.8 ± 0.3
Range
[14.5, 15.1]
Relative error
2.03%
Rule (add/sub)
δz = δa + δb
Rule (mul/div)
δz/z = δa/a + δb/b
Frequently Asked Questions
Significant figures represent measurement precision. A ruler measuring to 0.1 mm gives results with 4 sig figs (e.g. 15.32 mm). More sig figs = more precise measurement. Never report more sig figs than your measurement instrument provides.
Never. 0.00450 has 3 sig figs (4, 5, 0). The zeros before 4 are just placeholders. In scientific notation: 0.00450 = 4.50×10⁻³ — clearly 3 sig figs.
Find the 3rd sig fig, look at the 4th: if ≥5, round up; if <5, keep. Examples: 45,678 → 45,700 | 0.002345 → 0.00235 | 3.987 → 3.99 | 100,400 → 100,000.
The result has as many sig figs as the least precise factor. 6.38 (3 sf) × 2.1 (2 sf) = 13.398, reported as 13 (2 sf). This is because 2.1 is only known to 2 sig figs.
Round to the fewest decimal places, not sig figs. 123.4 + 0.567 = 123.967, reported as 124.0 (1 decimal place, matching 123.4). The measurement 123.4 has no hundredths precision.