# Significant Figures Calculator

> Significant figures calculator: round any number to your chosen sig figs with step-by-step counting rules shown. Free, runs locally in your browser, no signup.

- **Canonical URL:** https://boringtoolskit.com/significant-figures-calculator/
- **Category:** Chemistry
- **Evidence level:** authored-methodology
- **Reviewed:** September 2026
- **Last verified:** 2026-10-12
- **Privacy:** Inputs and results stay in this browser unless the page clearly labels an external request.

## How it works

Rounds a number v to sig significant figures: digits = floor(log10(|v|)); factor = 10^(digits - sig + 1); result = Math.round(v / factor) * factor, then formatted with toLocaleString('en-US', maximumFractionDigits 8). Scientific notation: mantissa = (v / 10^digits).toFixed(sig - 1), exponent = digits.

## Worked example

Input 12345 with 3 significant figures. Step 1: log10(12345) = 4.09, so digits = 4. Step 2: factor = 10^(4 - 3 + 1) = 10^2 = 100. Step 3: 12345 / 100 = 123.45; Math.round(123.45) = 123. Step 4: 123 * 100 = 12300, shown as 12,300. Scientific notation: 1.23 x 10^4. A value of 0 returns 0 with 0 x 10^0 notation, since log10(0) is undefined and the code special-cases zero.

## Assumptions

- Math.round uses round-half-toward-positive-infinity: an exact .5 tie rounds -2.5 to -2, not -3, because JavaScript's round is asymmetric for negatives.
- Binary floating point means stored values may sit just off a decimal midpoint (0.145 is really about 0.14499999999999999), so a tie can round down where decimal arithmetic would round up.
- The significant figures input must be a whole number from 1 to 15; 0, negatives, and values above 15 are rejected with an error, and an input of exactly 0 returns 0 with 0 x 10^0 notation.

## Common questions

### How do you round to significant figures?

Find the position of the first non-zero digit, count that digit plus the next sig-1 digits, then round at the following place. For 12345 to 3 significant figures, the last kept digit is the hundreds place, giving 12300.

### What is a significant figure?

A significant figure is any digit that carries meaning in a number: all non-zero digits, zeros between non-zero digits, and trailing zeros after a decimal point. Leading zeros, like the 0.00 in 0.00456, are placeholders and not significant.

### How many significant figures does 0.00456 have?

Three: the 4, 5, and 6. The leading zeros only locate the decimal point and do not count, so 0.00456, 0.0456, and 45600 written this way can all carry three significant figures.

### How does the calculator handle negative numbers?

It rounds the magnitude the same way and keeps the sign, but JavaScript's Math.round breaks .5 ties toward positive infinity, so -2.5 rounds to -2, not -3. Numbers without an exact tie behave normally, such as -12345 to 3 sig figs giving -12,300.

### Why does 0.145 round to 0.14 instead of 0.15?

In binary floating point, 0.145 is stored as approximately 0.14499999999999999, so it falls below the true midpoint and rounds down at 2 significant figures. The calculator shows what JavaScript's arithmetic actually computes rather than an idealized decimal result.

### What is the difference between rounding to decimal places and to significant figures?

Decimal-place rounding fixes the absolute position, like the hundredths place, regardless of the number's size. Significant-figure rounding keeps a fixed count of meaningful digits, so 12345 to 2 sig figs is 12,000 while 0.012345 to 2 sig figs is 0.012.

### What are the calculator's input limits?

The significant figures field accepts whole numbers from 1 to 15; anything outside that range shows an error message. An input value of exactly 0 returns 0, since logarithms of zero are undefined, and the scientific notation output displays 0 x 10^0.

## Related tools

- /rounding-numbers-calculator/
- /scientific-notation-converter/
- /round-up-down-calculator/

## Sources

- [SI Units](https://www.nist.gov/pml/owm/metric-si/si-units)
- [Significant figures](https://en.wikipedia.org/wiki/Significant_figures)
- [Rounding Numbers](https://www.mathsisfun.com/rounding-numbers.html)

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