Significant Figures Calculator

Enter a mathematical expression to calculate with significant figures

Using the Significant Figures Calculator

Enter a mathematical expression and click 'Calculate' to get the result with proper significant figures. The calculator supports basic arithmetic operations: addition (+), subtraction (-), multiplication (×), division (÷), exponentiation (^), and square root (√).

Example expressions: 12.34 + 5.6, 2.50 × 3.14, 125.6 ÷ 4.2, 15.0 - 2.33, (12.5 + 8.0) × 2.1, √(16.0), 2.5², 100.0 ÷ 3.0, 1.23 + 4.567 + 8.9, 45.6 × 7.89 ÷ 2.1.

The calculator will show you the step-by-step solution, explaining how significant figures are determined and applied in each operation.

What are Significant Figures?

Significant figures (also called significant digits) are the digits in a number that carry meaningful information about the precision of the measurement. They include all non-zero digits, zeros between significant digits, and trailing zeros after a decimal point. Leading zeros are never significant.

Rules for Identifying Significant Figures

1. Non-zero digits are always significant

Examples: 123 has 3 significant figures, 4.56 has 3 significant figures

2. Zeros between significant digits are significant

Examples: 1002 has 4 significant figures, 50.3 has 3 significant figures

3. Leading zeros are never significant

Examples: 0.0052 has 2 significant figures, 0.123 has 3 significant figures

4. Trailing zeros after decimal point are significant

Examples: 12.30 has 4 significant figures, 5.400 has 4 significant figures

5. Trailing zeros without decimal point may be ambiguous

Examples: 1200 could have 2, 3, or 4 significant figures depending on context

Calculation Rules

Addition and Subtraction

The result should have the same number of decimal places as the number with the fewest decimal places.

Example: 12.34 + 5.6 = 17.9 (not 17.94, because 5.6 has only 1 decimal place)

Multiplication and Division

The result should have the same number of significant figures as the number with the fewest significant figures.

Example: 12.34 × 5.6 = 69 (not 69.104, because 5.6 has only 2 significant figures)

Mixed Operations

When combining different operations, apply the rules in order of operations, keeping extra digits in intermediate calculations and rounding only the final result.