What are significant figures?

Significant figures are the digits in a number that carry meaning contributing to its precision, including all digits except leading zeros.

How do I count significant figures?

The tool automatically counts significant figures and provides detailed explanations of the counting rules and methods.

Sig Figs Calculator

Enter a number or expression to count significant figures and choose the final precision

📝Mathematical Expression

💡 Keyboard shortcuts: Press Enter to view results, Escape to clear

🚀 Quick Examples

⌨️ Insert Operators

Round to significant figures

110

3 significant figures

Rounding uses nearest, with exact halfway ties going to the even digit. Displayed trailing zeros preserve the selected precision. Automatic rules cover unmixed addition/subtraction, unmixed multiplication/division, and a single base-10 log of a written number. Mixed operations, powers and ln require your own precision decision. Numbers are treated as measurements; exact constants are not identified automatically. Calculations retain up to 80 significant digits internally. Extreme cancellation can still lose information; use the result within the stated limits.

📊

Calculation Results

Expression-log(2.5e-4)

Raw Result

3.602059991327962390427477789448986053536379762924217082620854922254216378548849

🎯 Final Result (3 sig figs)

3.60

⚖️ Applied Rules

➕ Add/Sub Rule

Not applied

✖️ Mul/Div Rule

Not applied

📈 Log Rule

3.60 (2 decimals)

🔍

Sig Fig Analysis

💡 Tip: Logarithm rule: decimal places in result = sig figs in input

2.5e-4
2 sig figs

🎯 Rule Applied: Log rule → 2 decimal places in result

📏

Counting Rules

✓ Significant Digits

• Non-zero digits are always significant (1-9)
• Zeros between non-zero digits are significant (205 has 3 sig figs)
• Trailing zeros after decimal are significant (1.200 has 4 sig figs)

✗ Non-Significant Zeros

• Leading zeros are never significant (0.0025 has 2 sig figs)
• Whole-number trailing zeros are ambiguous; this tool assumes placeholders (100 has 1 sig fig). Use 100. or 1.00e2 to specify 3.

🔢 Calculation Rules

Addition/Subtraction: Round to least decimal places

12.34 + 1.2 = 13.5 (1 decimal place)

Multiplication/Division: Fewest sig figs

2.5 × 3.147 = 7.9 (2 sig figs)

Base-10 logarithms: Decimal places match argument sig figs

-log(2.5e-4) = 3.60 (2 decimal places)

Count digits and round a calculation

Enter a written number or expression, then choose 1–10 significant figures for the rounded result. The operand analysis preserves the precision you wrote: 0.00250 has three significant figures, 100. has three, and 1.00e2 has three. Plain 100 is ambiguous; this tool assumes its trailing zeros are placeholders and counts one.

Use a decimal point and e notation for scientific values, such as 1.20e-3. Supported operators are +, −, ×, ÷ and ^; parentheses and unary signs are supported. Powers associate to the right: 2^3^2 means 2^(3^2), while -2^2 means -(2^2). Write (-2)^2 when the negative sign belongs to the base.

Understand the automatic rule suggestions

For expressions containing only addition and subtraction, the result follows the least precise decimal position after expanding scientific notation. For example, 200.50 + 1.2 becomes 201.7. Expressions containing only multiplication and division use the fewest operand significant figures; 0.00250 × 3.40 becomes 0.00850.

A single base-10 log of a written number can use its argument's significant figures as result decimal places. The pH expression -log(2.5e-4) gives 3.60 under that convention. Mixed expressions, powers, ln and computed log arguments receive no automatic precision suggestion: choose final precision using measurement context, uncertainty and any required course rules.

The slider result is your chosen significant-figure rounding. A rule suggestion may use a different precision; the two outputs serve different purposes. Exact constants and measured values cannot be distinguished from the expression alone, so exact conversion factors require your own precision decision.

Rounding convention and calculation limits

The calculator rounds to the nearest value and uses an even retained digit for an exact halfway tie. Thus 92.85 to three figures is 92.8, while 92.95 is 93.0. Trailing zeros in the displayed and copied result preserve its precision. This convention follows the OpenStax chemistry rounding guidance; follow a different convention if your assignment requires it.

Calculations use decimal arithmetic with up to 80 significant digits internally. That improves ordinary decimal calculations, but extreme cancellation can still lose information. Limits are 1,024 characters, 256 tokens, 30 digits per number and 32 nested operations. Scientific exponents must be between −300 and 300; nonzero values and intermediate results must remain within 1e−300 to 1e300 in magnitude. Power exponents are limited to −1,000 through 1,000.

Commas, units and implicit multiplication are not accepted. Write 2*(3+4), rather than 2(3+4). Division by zero and logarithms of nonpositive values show an error. Bare zero does not provide enough context to infer significant figures; decimal-place precision matters when reporting a zero measurement.

Read the significant-figures guide or review decimal and trailing-zero examples. Calculation inputs stay in the browser; website analytics and advertising are described in the privacy policy.

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How to Use

1
Enter Number or Expression
Type your number or mathematical expression in the input field. The tool will show significant figure analysis.
2
Configure Settings
Choose 1–10 significant figures for the final result. Exact halfway ties round to an even retained digit; automatic suggestions are separate from the chosen slider precision.
3
View Results
Review operand significant-figure counts, the chosen rounded result and any supported-rule suggestion. Read the stated assumptions and limits before using the result.

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📖

Significant Figures: Rules, Examples & Calculator Guide (2026)

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Frequently Asked Questions

What are significant figures?: Significant figures are the digits in a number that carry meaning contributing to its precision, including all digits except leading zeros.
How do I count significant figures?: The tool automatically counts significant figures and provides detailed explanations of the counting rules and methods.
Can I solve complex expressions?: Arithmetic supports unary signs, parentheses, powers, log, ln and scientific notation. Automatic precision suggestions cover unmixed addition/subtraction, unmixed multiplication/division and a single base-10 log of a written number. For mixed operations, powers, ln or exact constants, choose precision using measurement context.

Count digits and round a calculation

Understand the automatic rule suggestions

Rounding convention and calculation limits

🚀 Quick Examples

⌨️ Insert Operators

Calculation Results

⚖️ Applied Rules

Sig Fig Analysis

Counting Rules

✓ Significant Digits

✗ Non-Significant Zeros

🔢 Calculation Rules

Popular Use Cases

Count digits and round a calculation

Understand the automatic rule suggestions

Rounding convention and calculation limits

How to Use

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🚀 Quick Examples

⌨️ Insert Operators

Calculation Results

⚖️ Applied Rules

Sig Fig Analysis

Counting Rules

✓ Significant Digits

✗ Non-Significant Zeros

🔢 Calculation Rules

Popular Use Cases

Count digits and round a calculation

Understand the automatic rule suggestions

Rounding convention and calculation limits