Rounding Calculator

Rounding replaces a number with a simpler one that is close to it. This calculator rounds to a number of decimal places, to significant figures, or to the nearest ten, hundred, thousand or tenth. It uses exact arithmetic, explains which digit decides whether to round up or down, and shows the rounding error.

For "nearest", type 10, 100, 1000, 0.1 …
Try:

How to use the rounding calculator

  1. Enter the number.
  2. Choose decimal places, significant figures or nearest.
  3. Enter how many places (or 100, 1000 …) and press Calculate.

Formula

next digit≥5⇒round up\text{next digit} \ge 5 \Rightarrow \text{round up}

Worked example: 3.14159 to 2 d.p.

  • Number: 3.14159
  • Round to: Decimal places
  • How many / which place: 2

✓ Answer checked

3.143.14
Rounding error
0.001590.00159
Step-by-step working (3 steps)

  1. Find the last digit to keep

    Rounding to 2 decimal places keeps digits down to the 10^{-2} place.

    place value 10−2\text{place value } 10^{-2}

  2. Look at the next digit Round half up

    The next digit is 1. Less than 5: round down (keep).

    1<51 < 5

  3. Write the result

    Drop the remaining digits (keeping zeros as place holders where needed).

    3.143.14
How this was checked
  • ✓ The answer is a whole multiple of the rounding unit and within half a unit of the original.

Halves round away from zero (2.5 → 3, −2.5 → −3), the usual school rule.

Frequently asked questions

What is 3.14159 to 2 decimal places?

3.14, because the next digit, 1, is less than 5.

How do I round to significant figures?

Start counting at the first non-zero digit. 0.0045678 to 3 significant figures is 0.00457.

Does 2.5 round to 2 or 3?

This calculator rounds halves away from zero, so 2.5 becomes 3. Some systems round halves to the nearest even number instead.

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