Rounding Calculator
Round a number to a chosen number of decimal places.
Input sheet
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Rounding trims a number to a manageable number of decimal places — for money, measurements, or reporting — while staying as close as possible to the original value. This rounds to any chosen precision and also shows floor and ceiling.
How it works
Rounds to the chosen decimal places using round-half-up, and also shows floor and ceiling.
This tool uses round-half-up: when the digit being dropped is exactly 5, it rounds away from zero to the next value. It also reports the nearest whole number, the value rounded down (floor), and rounded up (ceiling).
Rounding to fewer decimal places introduces a small, bounded error, but accumulated rounding across many steps can drift, which is why precision-sensitive work rounds only at the end.
Rounded value = round(number × 10^places) ÷ 10^places
Worked examples
Rounding 3.14159 to 2 decimal places. → 3.14
The third decimal is 1 (less than 5), so the second decimal stays, giving 3.14.
Rounding 2.5 to 0 decimal places. → 3
With round-half-up, the dropped 5 rounds the value up to the next whole number, 3.
Tips & gotchas
- Round once, at the final step. Rounding intermediate results compounds error.
- Floor always rounds toward negative infinity and ceiling toward positive infinity, regardless of the half-up rule.
- For currency, round to 2 decimal places; for tolerances and engineering, match the precision your measurement tools actually support.
FAQ
What is round-half-up?
When the first dropped digit is exactly 5, the last kept digit increases by one (rounding away from zero). 2.5 becomes 3, and 2.45 to one place becomes 2.5.
What is the difference between floor, ceiling, and rounding?
Floor always goes down to the next whole number, ceiling always goes up, and rounding goes to whichever is nearer based on the dropped digits.
Why might rounding give a slightly different answer than I expect?
Some decimals cannot be stored exactly in binary, so a value like 2.675 may be held as 2.67499…, which can tip a half-up decision. Rounding only at the end minimizes this.
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