Significant Figures Calculator

Count written decimal digits and round with explicit half-even or half-away rules.

Count the digits actually written, flag ambiguous trailing integer zeros and round one decimal number without binary floating-point conversion. Scientific notation preserves the chosen output precision.

The original decimal digits stay in browser memory without uploads or persistence. Editing any field clears the prior output and download buttons. Already downloaded files are not deleted.

This tool runs entirely in your browser. Your data is never uploaded, never stored, and never leaves your device.

Count written decimal digits and round one number with explicit tie rules, ambiguous-zero warnings and precision-preserving scientific output.

How to use it

1Enter one decimal number or e notation without units or separators.
2Choose 1–100 output significant figures and the halfway rounding rule.
3Review the input count or ambiguity, scientific output and cautions.
4Download TXT or JSON containing the rule and explanation.

Example

Input: -1.250; 2 output figures; half to even
Output: 4 input figures; -1.2e+0 (ordinary decimal -1.2).

Half away from zero instead gives -1.3e+0. Neither rule determines measurement uncertainty.

What happens to your data

The original decimal characters are processed locally without uploads or persistence. Exports contain the input, chosen rule and precision cautions.

Last updated October 2026

Written zeros can carry information that disappears when a number is converted to ordinary floating-point form. This significant figures calculator reads the original decimal characters, counts meaningful written digits and rounds one number to a chosen number of significant figures. It accepts ordinary decimals and e notation while keeping the selected halfway rule visible.

Integer trailing zeros are not silently assigned a definite precision. The tool reports an ambiguity range for an input such as 1200, and scientific notation makes the requested output count explicit. Padding an answer with zeros changes its formatting, not the accuracy of a measurement. This is a digit-count and rounding aid, not an uncertainty calculator.

How it works

Enter one signed decimal number, optionally followed by an e exponent, such as 0.004500, 1200., 1.20e3 or -1.250. The sign and exponent do not add significant figures. Leading zeros before the first nonzero digit do not count. Zeros between nonzero digits do count. In a coefficient containing a decimal point, all digits from the first nonzero digit onward count, including its trailing zeros. The parser reads these characters directly and does not convert the coefficient to a binary floating-point number before rounding.

A plain integer ending in zeros does not state how many of those zeros were measured or merely placeholders. Thus 1200 is reported as ambiguous between two and four figures, rather than being presented as definitely two or definitely four. A decimal point or an explicit e coefficient removes that ambiguity under this tool's convention: 1200. has four figures, 1.2e3 has two and 1.200e3 has four. All written coefficient digits from the first nonzero digit count in e notation, including an integer coefficient such as 1200e0. Use the notation required by your course or reporting standard when its convention differs.

Choose an output count from 1 to 100. Digits are retained from the first nonzero digit, and the discarded decimal tail is compared with halfway. Half away from zero increases the magnitude on an exact tie: -1.25 becomes -1.3 at two figures. Half to even chooses the candidate whose final retained digit is even: the same input becomes -1.2. Values above or below halfway use the nearest candidate in either mode. Digits beyond an initial 5 matter; 1.2501 is above halfway at two figures, not an exact tie.

A carry can change the scientific exponent. For example, 9.995 rounded to three figures is 1.00e+1, equivalent to 10.0. The chosen three digits remain explicit in scientific notation. The ordinary decimal output is supplied for convenience, but an integer such as 1200 can again obscure whether its ending zeros are intended to be significant. Prefer the scientific field when communicating a specific output digit count.

If you request more digits than the input states, the result can be padded with zeros but a warning explains that this adds no measurement information. For an ambiguous integer, the warning uses the least-assumed count rather than silently choosing its most precise interpretation. The numerical value is still rounded from the exact entered decimal; ambiguity is about the claimed precision, not a different hidden input value.

An all-zero input has no first nonzero digit. Rather than inventing a finite significant-figure count, the tool reports that no count is inferred for zero, preserves the written place-value unit in its explanation and labels the output as a chosen zero format. For instance, 0.000 has a written decimal place-value unit of 1e-3; that fact alone is not an uncertainty interval. Negative zero is normalized to unsigned zero in the result.

The scope is rounding one decimal number. It does not add or multiply measured quantities, propagate uncertainty, distinguish exact constants from measured values, or certify laboratory accuracy. A scientific workflow may require uncertainty-based reporting rather than a mechanical digit-count rule. Avoid repeatedly rounding intermediate results when preparing a final calculation.

Input is limited to 200 characters and 128 coefficient digits, including entered zeros, with a written e exponent between -1000 and +1000. No thousands separators, units, Unicode multiplication notation, fractions, arithmetic expressions or special values such as Infinity are accepted. The calculation stays locally in browser memory. TXT and JSON exports include the input, rule, output, ambiguity and cautions. Editing a field removes the old result and download buttons; files already downloaded remain on your device.

Worked example: A negative exact tie under two rounding rules

Input: -1.250; request 2 significant figures
Result: Input has 4 figures. Half to even: -1.2e+0. Half away from zero: -1.3e+0.

Both outputs have two chosen significant figures. The selected rule determines the halfway result.

Common use cases

Compare half-even and half-away behavior on positive or negative halfway values.
Count written precision in small decimal numbers without losing trailing zeros.
Make the intended significant digits of a rounded large integer explicit with e notation.
Export a rounding explanation that retains ambiguous-input and added-precision warnings.

Frequently asked questions

How many significant figures are in 0.004500?＋

Four: 4, 5 and the two trailing zeros. The zeros before 4 set the decimal scale but are not significant figures. At three output figures the same numerical value is written 4.50e-3.

Is 1200 two or four significant figures?＋

Without an explicit convention, it is ambiguous. This tool reports a two-to-four range. Write 1.2e3 for two figures, 1.200e3 for four, or 1200. for four under the displayed decimal-point convention.

Why do the two halfway rules give different negative answers?＋

At a tie, half away from zero increases magnitude, so -1.25 becomes -1.3 at two figures. Half to even chooses -1.2 because the retained final digit 2 is even. These are selectable reporting rules, not floating-point glitches.

Can more output digits make my measurement more accurate?＋

No. Appending zeros is a formatting choice and cannot recover information that was not measured. The tool warns when the request exceeds the input's stated or least-assumed figure count.

Why does zero not receive a definite figure count?＋

All-zero notation requires context about resolution and measurement uncertainty. The tool keeps the written place-value unit in its explanation but does not infer a finite significant-figure count or an uncertainty interval from it.

Does this apply significant-figure rules to a whole expression?＋

No. It counts and rounds one entered decimal number. Addition, multiplication, exact constants and uncertainty propagation need their own calculation context and are outside this tool's scope.