Significant Figures Calculator

Calculate significant figures with precision and learn the theory behind them

Round to significant figures: (optional)
Quick Examples (Significant Figures)
7 — 1 significant figure (7) • decimals: 0
73 — 2 significant figures (7, 3) • decimals: 0
100 — 1 significant figure (1) • decimals: 0 Trailing zeros without a decimal are not significant.
673 — 3 significant figures (6, 7, 3) • decimals: 0
673.52 — 5 significant figures (6, 7, 3, 5, 2) • decimals: 2
0.0637 — 3 significant figures (6, 3, 7) • decimals: 4 Leading zeros are not significant.
30.00 — 4 significant figures (3, 0, 0, 0) • decimals: 2 Trailing zeros after a decimal point are significant.
0.0025 — 2 significant figures (2, 5) • decimals: 4
5.00 — 3 significant figures (5, 0, 0) • decimals: 2
1.200 × 103 — 4 significant figures (1, 2, 0, 0) In scientific notation, all digits in the mantissa (1.200) are significant.
1200 — typically 2 significant figures (1, 2) by default Ambiguous unless specified. 1200. → 4 sig figs; 1.200 × 103 → 4 sig figs.

Understanding Significant Figures

What are significant figures?

Significant figures (sig figs) are the digits in a number that convey real measurement precision. They tell you how confident you can be in a value. For example, 004 and 4 represent the same quantity, but 4.00 shows higher precision (three significant figures) because those zeros came from measurement, not padding.

Why it matters: in science, engineering, chemistry, and statistics, reporting the correct number of significant figures prevents false precision. Our Significant Figures Calculator counts sig figs, shows decimals, formats scientific notation, and applies rounding rules consistently so your results are both accurate and professional.

Rules for Identifying Significant Figures

These ARE significant
  • All non-zero digits (1–9). Example: 673 has 3 sig figs.
  • Zeros between non-zero digits. Example: 305, 3.604.
  • Trailing zeros in a decimal number. Example: 90.7500 has 6 sig figs.
  • All digits in the mantissa of scientific notation. Example: 1.200 × 103 has 4 sig figs.
These are NOT significant
  • Leading zeros before the first non-zero digit. Example: 0.00456 has 3 sig figs (4, 5, 6).
  • Trailing zeros in an integer without a decimal point (ambiguous unless clarified). Example: 1200 is typically treated as 2 sig figs (1, 2) unless written as 1200. or in scientific notation.

Tip: If a whole number’s trailing zeros are important, add a decimal point (e.g., 5000.) or use scientific notation (e.g., 5.000 × 103).

Examples

7 → 1 sig fig
73 → 2 sig figs
100 → 1 sig fig (no decimal)
673.52 → 5 sig figs
0.0637 → 3 sig figs
30.00 → 4 sig figs (2 decimals)
0.0025 → 2 sig figs (4 decimals)
1.200 → 4 sig figs
5000. → 4 sig figs (decimal clarifies)

Scientific notation examples: 1.23 × 105 has 3 sig figs; 7.00 × 10−3 has 3 sig figs (trailing zeros after the decimal are significant).

How to Round and Combine Significant Figures

  • Rounding to N sig figs: keep the first N significant digits and round the last one (0–4 down, 5–9 up). Example: 0.003678 to 2 sig figs → 0.0037.
  • Multiplication & Division: result has the fewest sig figs among inputs. Example: 2.4 (2 sig figs) × 3.15 (3 sig figs) = 7.6 (2 sig figs).
  • Addition & Subtraction: result keeps the fewest decimal places among inputs. Example: 12.30 (2 dp) + 0.456 (3 dp) = 12.76 (2 dp).
  • Logarithms: for log(x) or ln(x), the number of decimal places in the result typically equals the significant figures in x. Example: x = 3.20 (3 sig figs) → log(x) reported to 3 decimal places.

Good practice: keep guard digits during intermediate steps, then round once at the end to the correct precision.

Supported Operations

Use the keypad to enter your expression. The calculator counts significant figures, applies the correct rounding rules, and shows scientific notation:

  • Basic Operations: Addition (+), Subtraction (−), Multiplication (×), Division (÷)
  • Advanced: Exponent (^), Common logarithm (log), Natural logarithm (ln)
  • Grouping: Parentheses ( )
  • Constant: Euler’s number (e)

Tip: The calculator understands implicit multiplication: writing 8log(10) or 2(3+4) is treated as 8 × log(10) and 2 × (3+4).

Significant Figures Calculator — FAQs

Significant figures (sig figs) are the digits that communicate a measurement’s precision. Reporting the correct number of sig figs prevents false precision in lab reports, chemistry calculations, engineering tolerances, and scientific writing. Our calculator automatically counts sig figs, decimals, and formats scientific notation so your results are accurate and consistent.

  • Leading zeros are not significant: 0.0045 → 2 sig figs.
  • Sandwiched zeros (between non-zeros) are significant: 305 → 3 sig figs.
  • Trailing zeros in a decimal are significant: 30.00 → 4 sig figs.
  • Trailing zeros in a whole number without a decimal are ambiguous: 1200 is commonly treated as 2 sig figs unless you write 1200. (4 sig figs) or use scientific notation (e.g., 1.200 × 10³ for 4 sig figs).

Keep the first N significant digits and round the last kept digit: 0–4 down, 5–9 up. Example: 0.003678 to 2 sig figs → 0.0037. In the calculator, use the “Round to significant figures” buttons (1–5 or Auto).

  • Addition/Subtraction: result keeps the fewest decimal places among inputs.
  • Multiplication/Division: result keeps the fewest significant figures among inputs.

Tip: Keep guard digits during intermediate steps; round once at the end.

For log(x) and ln(x), a common convention is that the number of decimal places in the result equals the significant figures in x. Example: x = 3.20 (3 sig figs) → report log(x) to 3 decimal places. The calculator applies this convention and supports implicit multiplication (e.g., 8log(10) means 8 × log(10)).

Use scientific notation to unambiguously show precision in very large/small numbers or when trailing zeros matter. Example: 1200 → 1.200 × 10³ (4 sig figs). The calculator displays a scientific-notation line in every final answer.

Yes. Enable “Show previous results” to display each calculation as its own card in descending order (newest on top). Each card shows the expression, tokens, propagated sig-fig logic, the final rounded answer, and a one-click copy button.

Different courses may use slightly different conventions. Use the **Auto** mode for standard rules, or override with the 1–5 sig-fig buttons to match your rubric. You can still show full precision in steps and round your final line as required.