Significant Figures Calculator
Identify significant digits, round to target precision, and execute operations with measurement rules.
Sig Fig Breakdown & Rules Applied
The 5 Fundamental Rules of Significant Figures
Significant figures (sig figs) indicate the precision of measured physical quantities. The standard scientific rules are:
For deeper analysis and related planning, you can also explore our Area Calculator and Average Calculator.
- Rule 1 (Non-Zero Digits): All non-zero numbers ($1$ through $9$) are always significant. (e.g. $489$ has $3$ sig figs).
- Rule 2 (Captive Zeros): Zeros appearing between non-zero digits are always significant. (e.g. $2005$ has $4$ sig figs).
- Rule 3 (Leading Zeros): Zeros appearing in front of the first non-zero digit are merely place holders and are never significant. (e.g. $0.0025$ has only $2$ sig figs).
- Rule 4 (Trailing Zeros with Decimal): Trailing zeros in a number containing a decimal point are significant, because they indicate precision. (e.g. $8.500$ has $4$ sig figs).
- Rule 5 (Trailing Zeros without Decimal): Trailing zeros in integers without a written decimal point are ambiguous and generally counted as insignificant unless scientific notation specifies otherwise. (e.g. $4500$ is conventionally $2$ sig figs, while $4.500 \times 10^3$ is $4$ sig figs).
Arithmetic Operations with Significant Figures
When performing laboratory calculations, you must never present a final answer with more precision than your least precise initial measurement:
- Addition & Subtraction (Decimal Places Rule): The result cannot have more decimal places than the input with the least decimal places. $$\text{Example: } 125.17\text{ cm} + 2.3\text{ cm} = 127.47\text{ cm} \rightarrow \mathbf{127.5\text{ cm}}$$
- Multiplication & Division (Least Sig Figs Rule): The result cannot have more significant figures than the input with the lowest significant figure count. $$\text{Example: } 3.42\text{ cm} \times 0.21\text{ cm} = 0.7182\text{ cm}^2 \rightarrow \mathbf{0.72\text{ cm}^2} \text{ (2 sig figs)}$$
Frequently Asked Questions
What are the rules for counting significant figures?
1. All non-zero digits are significant. 2. Zeros between non-zero digits (captive zeros) are significant (e.g. 1002 has 4 sig figs). 3. Leading zeros before the first non-zero digit are not significant (e.g. 0.005 has 1 sig fig). 4. Trailing zeros in a number with a decimal point are significant (e.g. 50.00 has 4 sig figs). 5. Trailing zeros in an integer without a decimal point are ambiguous and generally considered not significant (e.g. 1200 has 2 sig figs).
How do significant figures work in addition and subtraction?
In addition and subtraction, the final result can have no more decimal places than the measurement with the fewest decimal places. For example, 12.52 + 3.1 = 15.62, which rounds to 15.6 (one decimal place).
How do significant figures work in multiplication and division?
In multiplication and division, the final answer must have the same number of significant figures as the measurement with the fewest significant figures. For example, 4.5 (2 sig figs) × 3.25 (3 sig figs) = 14.625, which rounds to 15 (2 sig figs).