Calculators

Rounding calculator

This rounding calculator rounds a decimal number to decimal places, significant figures or a custom increment. Pick one of six rules under Rounding rule: two Nearest rules that differ only on ties, Toward zero, Away from zero, Ceiling and Floor. It runs in your browser using exact decimal arithmetic, with no floating-point rounding error.

Result

Choose your settings, then select Round number to see the result and explanation.

Exact value, normalized display. Trailing zeros are omitted: 1.10 displays as 1.1. Very large or small magnitudes use scientific notation without losing digits. The selected step records the rounding precision; the displayed number does not describe measurement uncertainty.

How to use the rounding calculator

Type a decimal, integer or scientific notation such as -2.5e8 in Number to round. Under Round to, choose Decimal places, Significant figures or Increment; the field beneath it and its help text change to match.

For Decimal places, 2 rounds to hundredths, 0 to whole numbers, 1 to tenths and -1 to tens (47 becomes 50). For Significant figures, enter a whole number of 1 or more, counted from the first nonzero digit. For Increment, enter a positive decimal such as 0.05, 0.25 or 25.

Under Rounding rule, choose Nearest with either tie rule, Toward zero, Away from zero, Ceiling or Floor; the help text below it shows a worked example for the selected rule. Select Round number.

The result names the Selected step and explains which neighbor the rule chose. Download report saves the same text to rounding-calculation.txt.

How the tie rules and directional rules differ

Nearest, ties away from zero picks the closer multiple, and an exact tie moves away from zero: 2.5 rounds to 3, and -2.5 rounds to -3. Nearest, ties to even also picks the closer multiple, but a tie goes to the even multiplier instead: 2.5 rounds to 2, 3.5 rounds to 4, and -2.5 rounds to -2.

With a 0.05 increment, 0.125 rounds to 0.1 under ties to even, because 2 is the even multiplier. Ceiling always moves toward positive infinity unless the value is already exact, so -1.2 rounds to -1. Floor always moves toward negative infinity, so -1.2 rounds to -2.

Toward zero drops the extra digits, so -1.27 at one decimal place rounds to -1.2. Away from zero increases the distance from zero unless the value already matches the step, so -1.21 at one decimal place rounds to -1.3.

Limits

The calculator rounds to decimal places, significant figures or a custom increment, using six rounding rules; it does not average, sum or combine numbers. Input must be digits with a dot for decimals, or scientific notation such as -2.5e8; commas, spaces inside the number, and percent or currency signs are rejected.

Decimal places must be a whole number, positive, zero or negative; significant figures must be a whole number of 1 or more; an increment must be a positive decimal greater than zero. Trailing zeros are omitted in the display, so 1.10 shows as 1.1, and the exact value drives every rounding decision, not a displayed approximation.

There is no fixed digit cap; the math uses exact decimal arithmetic rather than floating point, so 1.005 rounds to 1.01 at two decimal places instead of the 1.00 a naive floating-point calculation can produce. A demanding custom increment or a very large number can exceed the browser's available memory, and Cancel stops a calculation that is taking too long.

Questions

How do I get a calculator to round up?

Choose Ceiling (toward +∞) under Rounding rule and set Decimal places to 0 to round up to a whole number. At any other Decimal places, Ceiling still moves toward positive infinity, but to the next step up for that precision: 2.13 at one decimal place rounds up to 2.2.

Is 7.5 rounded to 7 or 8?

Both Nearest rules round 7.5 to 8. Ties away from zero moves the tie up, and ties to even also picks 8 because 8 is even. The two rules differ on 6.5, which ties to even rounds to 6. The directional rules give 7 with Toward zero and Floor, and 8 with Away from zero and Ceiling.

How do I round decimal places?

Under Round to, choose Decimal places, then enter the count in the field below: 2 for hundredths, 0 for whole numbers, or -2 for hundreds. Choose a Rounding rule, then select Round number. The result panel shows the exact rounded value and an explanation of which rule applied.

How do decimal places and significant figures differ?

Decimal places count digits from the decimal point; significant figures count from the first nonzero digit. For 0.012345, two decimal places gives 0.01, while two significant figures gives 0.012. Negative decimal places round to tens, hundreds and larger powers of ten; zero stays zero at every precision.

Is 7 rounded to 5 or 10?

To the nearest 5, 7 rounds to 5, because it is 2 away from 5 and 3 away from 10: choose Increment and enter 5. To the nearest 10, it rounds to 10: choose Decimal places and enter -1. Any positive increment works, such as 0.05 or 25; a zero or negative increment is rejected.