How to use the Rounding Calculator
- Enter the number to round.
- Choose decimal places, significant figures or nearest multiple.
- Enter the number of places or figures, or the multiple.
- Compare the five results.
Formula used
To round to d decimal places, scale by 10^d, round to a whole number and scale back. For significant figures the places are 1 − the position of the first digit. For a multiple m: round(x ÷ m) × m.
Worked example
Here is the Rounding Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| Number | 3.142 |
| Round to | Decimal places |
| Places, figures or multiple | 2 |
| Result | |
| Rounded (half away from zero) | 3.14 |
| Banker’s rounding (half to even) | 3.14 |
| Rounded up (toward +∞) | 3.15 |
| Rounded down (toward −∞) | 3.14 |
| Truncated (toward zero) | 3.14 |
The five rules
The standard rule, half away from zero, sends a tie to the larger size: 2.5 becomes 3. Banker’s rounding sends a tie to the nearest even number, so 2.5 becomes 2. Rounding up (toward positive infinity) gives 3 for 2.5 and rounding down gives 2. Truncation just drops the extra digits.
Negative numbers show the differences clearly. For −2.5, the standard rule gives -3, banker’s gives -2, rounding up gives -2, rounding down gives -3 and truncation gives -2.
Decimal places and significant figures
Decimal places count digits after the point. Significant figures count meaningful digits from the first non-zero one. Rounding 1234.5678 to 3 significant figures gives 1230, because the first three significant digits are 1, 2 and 3.
Negative decimal places round to tens, hundreds and so on. Rounding 1234 to −2 decimal places gives 1200.
Rounding to a multiple
To round to the nearest 5, 10, 0.25 or any other multiple, choose the nearest-multiple option. 17 rounded to the nearest 5 is 15. Rounding up gives 20 and rounding down gives 15.
This is handy for pricing, tolerances and time slots, for example rounding minutes to the nearest 15.
Which rule should you use?
School and everyday work normally use the half-up rule. Banker’s rounding is common in accounting and in some software, because it avoids a steady upward drift when many halves are rounded. Rounding up suits quantities such as the boxes you need to buy, and truncation suits cases where you must never overstate.
Round only at the end of a calculation. Rounding at each step builds up errors that the final answer carries.
Common mistakes when rounding
The most common error is rounding too early. If you round each step of a long calculation, small errors add up. Keep full precision until the final answer, then round once to the number of places the problem asks for.
Another is confusing decimal places with significant figures. 0.004567 to 2 decimal places is 0.00, which is useless, while to 2 significant figures it is 0.0046. Choose the method that keeps the information that matters.
Frequently asked questions
What is banker’s rounding?
It rounds a tie to the nearest even digit, so 2.5 goes to 2 and 3.5 goes to 4.
How do I round to the nearest 10?
Choose the nearest multiple option and enter 10, or use −1 decimal places.
What is the difference between truncating and rounding down?
They agree for positive numbers. For negatives, truncating moves toward zero and rounding down moves away from it.
How many significant figures are in 0.00120?
Three: 1, 2 and 0. Leading zeros do not count.
Why is 1.005 rounded to 1.01?
The calculator treats the number as typed, so 1.005 is a tie and rounds up. Many programs show 1.00 because of binary storage.
Can it round negative numbers?
Yes. Each rule treats negatives as described above.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.