Rounding Calculator
Round a number to a chosen number of decimal places — or to the nearest ten, hundred or thousand — and choose exactly how ties are broken.
Calculator
- Any decimal place (including negatives)
- Half-up and banker’s rounding
- Floor, ceiling, truncate
- States the rule applied
Result & calculation receipt
- Method
- Rounding to 2 decimal place(s) using round half up
- Formula
round(value × 10^places) ÷ 10^places- Substitution
- round(3.14159 × 10^2) ÷ 10^2 = round(314.159) ÷ 100 = 3.14
- Steps
- Shift the decimal point: 3.14159 × 10^2 = 314.159
- Apply "round half up" to 314.159 → 314
- Shift back: 314 ÷ 10^2 = 3.14
- Verification
- The rounded value differs from the original by 0.001590000001, at most half a unit in the last kept place.
- Exact result
- 3.14
- Decimal result
- 3.14
- Engine
- math-solvers v1.4.0
How this calculator works
The value is scaled by ten to the power of the number of places, the chosen rule is applied to the scaled integer, and the value is scaled back. Round-half-up sends a trailing .5 away from zero; banker’s rounding sends it to the nearest even digit to remove long-run bias; floor and ceiling always go down or up; truncation simply drops the extra digits. The steps show the scaled value and the rule that fired.
Worked example
Rounding 3.14159 to two decimal places multiplies by 100 to get 314.159, rounds to 314, and divides back to 3.14. A negative place count rounds to the left of the decimal point: 1234 with −2 places rounds to 1200. And 2.5 with banker’s rounding becomes 2, because 2 is the nearer even number, while ordinary half-up would give 3.
Key insight
The rounding rule matters more than people expect. Repeatedly rounding halves up biases a long column of figures upward; banker’s rounding cancels that bias, which is why spreadsheets and accounting systems often use it. Rounding is also not associative — round once to the final precision, not in stages.
Frequently asked questions
What is the difference between half-up and banker’s rounding?
Half-up always rounds a trailing 5 away from zero (2.5 → 3). Banker’s rounding (round half to even) sends a 5 to the nearest even digit (2.5 → 2, 3.5 → 4), which removes the upward bias when many numbers are rounded and summed.
How do I round to the nearest hundred?
Enter a negative number of decimal places. Places = −2 rounds to the nearest hundred, −3 to the nearest thousand. For example 1,234 with −2 places rounds to 1,200.
What is the difference between truncating and rounding down?
Truncating drops the extra digits toward zero, so −2.9 truncates to −2. Rounding down (floor) always goes toward negative infinity, so −2.9 floors to −3. For positive numbers the two agree.
Does rounding lose information?
Yes — rounding is deliberately lossy. The calculator reports how far the rounded value is from the original so you can see the size of the discarded part, which is at most half a unit in the last kept place.
Why not round in stages?
Rounding 2.446 to two places then one place gives 2.45 → 2.5, but rounding straight to one place gives 2.4. Always round once, to the final precision you need.
Methodology & verification
The value is multiplied by 10^places, the selected tie-breaking rule is applied (round half away from zero, round half to even, ceiling, floor or truncate toward zero), and the result is divided back by 10^places. Negative place counts round to tens, hundreds and beyond. Non-numeric values and non-integer place counts return structured errors. The receipt reports the absolute difference between the original and rounded value so the discarded magnitude is visible and never silently hidden.
Engine: math-solvers v1.4.0 · Last reviewed: · Every result is computed client-side and never sent to a server. See the verification methodology and the scientific calculator validation.