CalcArcade.

Rounding Calculator

Enter a number, choose how many places or significant figures and a method. You get the rounded value and a table of the result under every method.

Your numbers

Result

How we calculate it

The calculator works on the digits you type, not on a computer approximation of them. It looks at the digits that will be dropped and compares them with half. Below half rounds down and above half rounds up. Exactly half is a tie, and the method decides it: half away from zero rounds 2.5 to 3 and −2.5 to −3, half to even rounds to the nearest even digit (2.5 to 2, 3.5 to 4), and half up always goes toward positive infinity (2.5 to 3 and −2.5 to −2).

Ceiling, floor, truncate and away from zero ignore the half and always go one way. For example 1.005 to two decimal places is 1.01 by half away from zero and 1.00 by half to even. Rounding to significant figures counts digits from the first non-zero digit, so 0.00123456 to three figures is 0.00123 and 123456 is 123000.

Assumptions and limits

  • Because the digits are used exactly, 1.005 is a true tie. Some programs give 1.00 because they store 1.005 as a binary number a hair below it.
  • A negative number of places rounds to tens (−1), hundreds (−2) and so on. Zeros that the rounding leaves are kept, so 2 to three places is 2.000.
  • You can type up to 40 digits and an exponent such as 1.5e3 (within ±60).

Frequently asked questions

How do you round 2.5?

It depends on the method. The usual school rule, half away from zero, gives 3. Banker's rounding (half to even) gives 2. The table shows the answer for every method.

What is banker's rounding?

Round half to even sends a tie to the nearest even digit, so 2.5 becomes 2 and 3.5 becomes 4. Over many numbers the ties go up and down equally often, which avoids a small upward bias.

How do I round to significant figures?

Count digits from the first one that is not zero and keep that many. 0.004567 to two significant figures is 0.0046, and 45,678 to two is 46,000.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Number to round = 3.14159; Round to = Decimal places; Decimal places (negative for tens, hundreds) = 2; Method = Round half away from zero (usual school rounding).

  • Rounded value 3.14
  • Rounded to 2 decimal places
  • Method Round half away from zero

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.