Rounding calculator — decimal places, sig figs or nearest multiple

How to use the rounding calculator

1. Type the value in Number. Scientific notation such as 1.2e-5 is accepted.
2. In Round to, choose Decimal places, Significant figures or Nearest multiple (0.05, 5, 100…).
3. Fill in the box that appears: the number of places, the number of significant figures, or the multiple.
4. Pick a Rounding rule. Half up is the usual school rule.
5. Read Rounded and the Rounding error, then compare all rules in the Every rounding rule table.

What it does and when to use it

Rounding shortens a number while keeping it close to the original. You round money to cents, measurements to the precision of your instrument, and estimates to the nearest hundred. The tricky part is the rule for exact halves and for negative numbers, where textbooks, spreadsheets and programming languages do not all agree.

This page lets you see every rule side by side, which is handy when checking homework or matching a system’s output. For counting significant figures in a measured value, use the significant figures calculator; for turning a long decimal into a fraction, try the decimal to fraction converter.

How it works

The number is stored as an exact fraction. To round to p decimal places, the tool multiplies by 10^p, rounds to a whole number with the chosen rule, and divides by 10^p again. Negative p uses the same idea with 10, 100 and so on. Significant figures are converted to decimal places from the position of the first non-zero digit. For a multiple m, the tool rounds x ÷ m to a whole number and multiplies back by m.

These rows are the tool’s own results for 2.5 and −2.5 rounded to 0 places.

Step by step: 7.33 to the nearest 0.05:

1. Divide by the multiple: 7.33 ÷ 0.05 = 146.6.
2. Round to a whole number with half up: 147.
3. Multiply back: 147 × 0.05 = 7.35.
4. Rounding error: 7.35 − 7.33 = 0.02.

Worked examples

Two decimal places. 2.675 with half up gives Rounded: 2.68, plus a note that floating-point toFixed would give 2.67.

Banker’s rounding. 2.5 to 0 places with half to even gives 2, with Rounding error: -0.5.

Nearest 5 cents. 7.33 to the multiple 0.05 gives Rounded: 7.35.

Nearest hundred. 1234.5 with −2 decimal places gives Rounded: 1200. With the Up or Ceiling rule the table shows 1300.

Limits and tips

• Round only once, at the end. Rounding in each step of a calculation lets errors build up.
• Decimal places can go from −15 to 50.
• When estimating percentages, round the final figure from the percentage calculator rather than the inputs.
• All rounding happens in your browser.