Rounding, done exactly
Rounding trims a number to the precision you need: two decimal places for money, a few significant figures for a measurement, the nearest 5 for a quick estimate. Most of the time it is simple, but numbers that sit exactly halfway, like 2.5, can go either way depending on the rule.
This rounding calculator rounds to decimal places, significant figures or the nearest multiple, using any of six rules, and lists what every rule gives so you can see the difference. It works on the exact digits you type, so 1.005 rounds to 1.01 as it should, rather than slipping to 1.00 the way some computer rounding does.
How to use it
- Choose decimal places, significant figures or nearest multiple.
- Type the number, then how many places or figures, or the multiple such as 5, 10 or 0.25.
- Pick a rounding rule. Half up is the one taught in school.
- Read the answer, and compare the other rules in the list underneath.
The rounding rules
half up: a 5 rounds away from zero (2.5 → 3, −2.5 → −3)
half to even: a tie goes to the even digit (2.5 → 2, 3.5 → 4)
up (ceiling) and down (floor): toward +∞ or −∞, whatever the digits
truncate: simply drop the extra digits (toward zero)Half to even, also called banker’s rounding, is used in some accounting and statistics because it does not drift upward over many roundings: ties go up half the time and down half the time.
Worked example: 2.345 to two decimal places
- The digit after the second place is 5, followed by nothing, so it is an exact tie
- Half up: 2.35
- Half to even: the 4 is already even, so 2.34
- Floor and truncate: 2.34; ceiling: 2.35
Rounded half up, 2.345 becomes 2.35; with banker’s rounding it becomes 2.34. For a number that is not a tie, such as 2.346, every rule except floor and truncate gives 2.35.
Every rule side by side
| Number | Half up | Half even | Half down | Up | Down | Truncate |
|---|---|---|---|---|---|---|
| 2.5 to 0 places | 3 | 2 | 2 | 3 | 2 | 2 |
| 3.5 to 0 places | 4 | 4 | 3 | 4 | 3 | 3 |
| −2.5 to 0 places | −3 | −2 | −2 | −2 | −3 | −2 |
| 2.45 to 1 place | 2.5 | 2.4 | 2.4 | 2.5 | 2.4 | 2.4 |
| 2.55 to 1 place | 2.6 | 2.6 | 2.5 | 2.6 | 2.5 | 2.5 |
Note how the rules split only on ties and on negative numbers. For most everyday numbers they agree.
Significant figures and multiples
- Significant figures count from the first non-zero digit: 0.0012345 to 2 figures is 0.0012.
- Trailing zeros after a decimal point are significant: 1.500 shows four figures.
- Rounding to the nearest 0.05 or 0.25 is common for prices and measurements.
- For very large or small numbers, the scientific notation calculator shows the figures clearly.
Frequently asked questions
How do I round to two decimal places?
Look at the third decimal place. If it is 5 or more, add one to the second place; if it is less than 5, leave it. Then drop everything after the second place. So 3.14159 becomes 3.14, and 2.675 becomes 2.68. The calculator does this exactly, digit by digit.
What is banker’s rounding?
Banker’s rounding, or half to even, rounds an exact tie to the nearest even digit: 2.5 becomes 2 and 3.5 becomes 4. Because ties go up and down equally often, totals of many rounded numbers do not drift upward. Numbers that are not exact ties round as usual.
How do I round to significant figures?
Start counting at the first digit that is not zero, keep the number of figures you need, and round the last one. So 0.0012345 to two significant figures is 0.0012, and 123,456 to three is 123,000. Choose Significant figures above to do it for any number.
How do I round to the nearest 5?
Divide by 5, round to a whole number, then multiply by 5 again. So 17 ÷ 5 = 3.4, which rounds to 3, giving 15; and 18 rounds to 20. Choose Nearest multiple above and enter 5, or any other step such as 10, 0.25 or 100.
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