What are significant figures?

Digits that carry meaning for measurement precision; all non-zero digits, zeros between non-zero digits, and trailing zeros in decimal numbers are significant.

Do trailing zeros count?

Trailing zeros are significant if a decimal point is present (e.g., 2.300 has 4 sig figs). Without a decimal point, trailing zeros are usually not significant (e.g., 2300 has 2 sig figs), unless explicitly indicated by notation.

Does the calculator accept scientific notation?

Yes. You can enter inputs such as 1.23e-4 or 6.02E23.

Which rounding modes are supported?

Round half up (5 rounds away from zero) and round half to even (banker’s rounding).

Is this consistent with metrology standards?

The rules align with NIST SP 811 guidance on significant figures and scientific notation.

Significant Figures Calculator

This professional-grade calculator counts significant figures and rounds any number to a chosen number of significant digits. It accepts integers, decimals, and scientific notation (e.g., 1.23e-4), and explains each step so you can verify results with confidence. Ideal for students, scientists, engineers, and anyone working with measurement precision.

Calculator

Count significant figures

Round to N significant figures

Number *

Accepts scientific notation (e.g., 1.23e-4). Ignores thousands separators.

Trailing zeros behavior

Results

Enter a number and choose an operation to see results here.

Data Source and Methodology

Authoritative Source: NIST Special Publication 811, Guide for the Use of the International System of Units (SI), 2008 Edition (Rev. 2008, update 2019), National Institute of Standards and Technology. Direct link: NIST SP 811.

All calculations strictly follow the rules and definitions described in this source.

The Formula Explained

Significant digits (definition):

• Nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros are significant if and only if a decimal point is present (standard rule).

Rounding to N significant figures:

1) Normalize: \( x = m \times 10^{e} \) with \( 1 \le |m| < 10 \).

2) Round \( m \) to N digits using the chosen rule (half-up or half-even).

3) Denormalize: \( \tilde{x} = \tilde{m} \times 10^{e} \).

Glossary of Variables

Input number: The value to analyze (integer, decimal, or scientific notation like aEb).
Significant digits (N): Target precision for rounding.
Rounding mode: Half-up or half-to-even rule for midpoint cases.
Normalized form: Scientific notation \( m \times 10^{e} \) with \( 1 \le |m| < 10 \).
Sig-fig count: Number of significant digits in the input under the selected trailing-zero convention.

How It Works: A Step-by-Step Example

Example: Input 0.00456090, round to N = 3 with half-up.

Normalize: \( 0.00456090 = 4.56090 \times 10^{-3} \).
Keep first 3 digits → 4.56, next digit = 0 < 5 → no increment.
Result: \( 4.56 \times 10^{-3} = 0.00456 \).

Frequently Asked Questions (FAQ)

How do I count significant zeros?

Leading zeros are never significant; zeros between non-zero digits always are; trailing zeros are significant only if a decimal point is present (standard rule).

What about whole numbers like 2300?

By default, 2300 has 2 significant digits. If the precision is intended to be higher, use scientific notation (e.g., 2.300×10³ has 4 sig figs) or enable the override.

What is half-even rounding?

Also called banker’s rounding: midpoints (5) round to the nearest even last kept digit, reducing systematic bias.

Does the calculator keep trailing zeros after rounding?

Yes—when they are significant by rule or when necessary to reflect the requested N significant digits.

Can I paste values with commas?

Yes. Thousands separators are ignored during parsing.

Is this appropriate for lab reports?

Yes. It follows metrology conventions compatible with NIST SP 811; always confirm local or journal-specific styles.

Tool developed by Ugo Candido. Content verified by the CalcDomain Editorial Team.
Last reviewed for accuracy on: September 21, 2025.