Rounding Calculator
Round once to a chosen decimal place or to the nearest multiple, using nearest, floor, ceiling or half to even.
Result
Rounded value: 1,234.57
The value is rounded once; the selected rule is shown explicitly.
- Signed rounding difference
- 0.003
- Absolute rounding difference
- 0.003
- Place value
- 0.01
https://calcgallery.com/everyday-math/rounding-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Rounding Calculator
- Enter the number, then choose whether to round to a decimal place or to a multiple.
- For a decimal place, enter how many to keep; use a negative count for tens, hundreds or larger positions. For a multiple, enter the step, such as 5 or 0.25.
- Choose nearest, floor, ceiling or half to even and read the signed rounding difference.
Name the rule and round once
Rounding is not one universal operation. Nearest chooses the closest retained place, taking a tie toward positive infinity; half to even takes a tie to the even neighbour; floor moves toward negative infinity; ceiling moves toward positive infinity.
decimal place result = rule(value × 10^places) ÷ 10^placesmultiple result = rule(value ÷ step) × stepThe calculation is applied directly at the requested place or step. NIST Handbook 44 warns against successive rounding, which is why this interface rounds once and states its convention explicitly.
Half to even
For measurement work, NIST SP 811 (section B.7.1) says that when the digits dropped are a 5 followed only by zeros, the digit before it stays if it is even and goes up by one if it is odd. The rule only changes true ties. 2.51 still rounds to 3, because the digits dropped are more than half.
Rounding to a multiple
Rounding to the nearest 5, 25 or 0.25 is the same operation as rounding to a decimal place, with the step in place of a power of ten. Every rule works with it: floor to a multiple of 12 gives the whole dozens, and ceiling to a multiple of a pack size gives the smallest quantity that fills whole packs.
With your numbers
- Scale 1,234.567 to the requested place, apply nearest once, then unscale.
- Rounded value = 1,234.57; difference = 0.003.
Quick reference
The value is rounded once; the selected rule is shown explicitly.
| Example | Rounded value |
|---|---|
| 1234.567 to two decimals | 1,234.57 |
| Nearest whole number | 19 |
| Floor to one decimal | 3.1 |
| Ceiling to one decimal | 3.2 |
| Round to hundreds | 1,300 |
| Negative floor | -2.4 |
| 2.5 half to even | 2 |
| 0.125 half to even, two decimals | 0.12 |
| 17 to the nearest 5 | 15 |
| 1.37 to the nearest quarter | 1.25 |
| 7.1 up to a multiple of 2 | 8 |
Common questions about the Rounding Calculator
- What does two decimal places mean?
- It retains the hundredths place, so 12.345 becomes 12.35 under the nearest rule.
- What does a negative decimal place mean?
- Minus one rounds to tens, minus two to hundreds and so on.
- How are exact halfway values handled?
- Nearest takes a half step toward positive infinity, so 2.5 becomes 3 and −2.5 becomes −2. Half to even takes it to the even neighbour instead, so 2.5 becomes 2 and 3.5 becomes 4. Select floor or ceiling when directional rounding is required.
- What is banker’s rounding?
- Another name for rounding half to even. A value exactly halfway is rounded to whichever neighbour is even. Because halves go up and down equally often, a long column of rounded figures does not drift upward the way it does when every half rounds up. NIST gives it as the rule for dropping a 5 followed only by zeros.
- How do I round to the nearest 5, 10 or quarter?
- Choose a multiple and enter the step. The number is divided by the step, rounded once to a whole number under the chosen rule, and multiplied back, so 17 to the nearest 5 is 15 and 1.37 to the nearest 0.25 is 1.25. Floor and ceiling give the multiple below or above.
- Why does 1.005 round to 1.01 here when some software gives 1.00?
- A computer stores 1.005 as a binary number a hair below it, so rounding the stored value gives 1.00. This page reads what you typed as a decimal: a result that misses a whole step or a half step only by that storage error counts as exactly on it, so 1.005 is a tie and rounds up. The same correction keeps 0.29 floored to two places at 0.29.
- Why round only once?
- Successive rounding can change the final answer. The calculator scales directly to the requested place and applies one rule once.