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Rounding Calculator

Round any number to a whole, decimal places, or the nearest 10/100/1000 — choose half-up, half-even, ceiling, floor or truncation.

Rounded value

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What the rounding calculator does

The rounding calculator rounds any number to the precision you choose: decimal places, the nearest whole, the nearest 10 / 100 / 1000, or any custom multiple. Pick from six rounding modes — half-up (the standard), half-even (banker's), half-down, ceiling, floor and truncation — and the tool also shows every mode at once so you can compare them side by side.

The six rounding modes

  • Half up — the textbook default. 2.5 → 3, 2.49 → 2, 2.51 → 3.
  • Half even (banker's) — used by most banks and statistics packages. 2.5 → 2, 3.5 → 4, 2.51 → 3. Avoids bias when many numbers are rounded.
  • Half down — the opposite of half-up at the tie: 2.5 → 2, 3.5 → 3.
  • Ceiling — always rounds upward (toward positive infinity). 2.1 → 3, −2.9 → −2.
  • Floor — always rounds downward (toward negative infinity). 2.9 → 2, −2.1 → −3.
  • Truncate — chops the digits, always toward zero. 2.9 → 2, −2.9 → −2.

Banker's rounding, in one sentence

When the next digit is exactly 5 and there is nothing after it, round to the even neighbour. So 2.5 rounds to 2 (because 2 is even), and 3.5 rounds to 4. Over many transactions this keeps the average rounding error near zero, while half-up adds a tiny positive bias because every tie goes the same way.

Rounding to a multiple

"Nearest 10" means rounding 47 to 50, 43 to 40, and 45 to 50 (half-up) or 40 (half-even). The same idea generalises: nearest 0.25 turns 1.13 into 1.25 and 0.06 into 0.0; nearest 0.05 is great for prices. The calculator's "Nearest multiple of…" mode lets you set any positive value.

The float problem

Computers store numbers in binary, and many decimal values (like 0.1) don't have an exact binary representation. So 0.1 + 0.2 evaluates to 0.30000000000000004 in nearly every programming language. Rounding usually hides this, but edge cases (like rounding 1.005 to two decimals) can surprise you because the underlying value is actually 1.00499999…. For currency, the safest approach is to do the maths in integer cents and only divide by 100 at the end.

When not to round

Don't round in the middle of a multi-step calculation if you can avoid it — small errors compound. Carry full precision through every step and only round the final value you display. For the same reason, store and transmit numbers at full precision; rounding is a presentation choice, not a storage choice.

Use with the other tools

For working with parts of 100, the percentage calculator handles the four common percent questions. For statistics with rounded summaries, the average calculator and standard deviation calculator are quick companions.

Frequently asked questions

What does it mean to round a number?

Rounding replaces a number with a nearby value that has fewer digits, making it easier to read or use. Standard rounding looks at the first digit you would drop: if it is 5 or more, round up; if it is 4 or less, round down.

What is the difference between half-up and half-even (banker's) rounding?

Half-up always rounds 0.5 upward (2.5 → 3, 3.5 → 4). Half-even rounds to the nearest even number when the digit is exactly 5 (2.5 → 2, 3.5 → 4). Half-even is the default in banking and many statistics programs because it eliminates bias when many numbers are rounded.

How do I round to a specific number of decimal places?

Pick "Decimal places" and enter how many digits after the point you want. The calculator multiplies, rounds, and divides back, which is the standard implementation used in most programming languages.

What is truncation?

Truncation simply chops off the unwanted digits without rounding. 3.78 truncated to whole becomes 3, not 4. It is faster than rounding but biased downward for positive numbers and upward for negative ones, so most accuracy-sensitive contexts prefer real rounding.

Why are floats imprecise when rounding?

Numbers like 0.1 cannot be represented exactly in binary, so 0.1 + 0.2 = 0.30000000000000004 instead of 0.3. Rounding usually papers over this, but very close-to-the-half cases (like 1.005 rounded to two places) can surprise you. For currency, calculate in integer cents to avoid the issue entirely.

When should I use rounding?

When precision beyond a certain digit doesn't help the reader (final invoice totals, scores, headlines), when you need to fit values into a display, or when an instrument's precision doesn't support more digits than that. Don't round intermediate results in a long calculation, though — that builds up rounding error.

Worked example

Round 3.14159:

  • To 2 decimal places, half-up: digit after is 1, so we round down → 3.14
  • To 3 decimal places, half-up: digit after is 5, so we round up → 3.142
  • To the nearest whole: 3 (next digit is 1)
  • To the nearest 10: 0 (and 3.14 to the nearest 100 is also 0)

A banker's-rounding example: 2.5 rounded to a whole gives 2, while half-up gives 3. Try both in the calculator and check the compare table to see every mode at once.

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