Your result will appear here
Fill in the fields and press Calculate.
Rounding trims a number to a chosen precision — but "round to 2" can mean two decimal places, two significant figures, or the nearest multiple of two, and they give different answers. This tool does all three, and also shows the round-up (ceiling) and round-down (floor) values.
Enter a number, pick how you want to round it, and set the precision.
Rounding Calculator: step-by-step worked example
- Number to round
- 1,234.5678
- Round to
- Decimal places
- Precision (places / figures / multiple)
- 2
- 1
Pick the multiplier
k = 10^places
10² = 100
- 2
Scale the number
x × k
1,234.5678 × 100 = 123,456.78
- 3
Round to the nearest integer
Fraction ≥ 0.5 rounds up, otherwise down
round(123,456.78) = 123,457
- 4
Divide back
Result = round(x × k) ÷ k
123,457 ÷ 100 = 1,234.57
- 5
Round up and round down
⌈x × k⌉ ÷ k · ⌊x × k⌋ ÷ k
= ↑ 1,234.57 · ↓ 1,234.56
- Rounds down
- Rounds up
Good to know: Because computers store decimals in binary, a value like 2.675 may round to 2.67 (it is really 2.67499…). In money calculations, round at the end, not at every intermediate step.
Rounding Calculator — how it works
Three ways to round
| Mode | "Round 12345.678 to 2" gives |
|---|---|
| Decimal places | 12345.68 |
| Significant figures | 12000 |
| Nearest multiple (of 2) | 12346 |
Decimal places keeps a set number of digits after the point. Significant figures keeps a set number of meaningful digits counting from the first non-zero one — the standard in science for expressing precision. Nearest multiple snaps to the closest 10, 5, 0.5, or whatever step you set.
Round-up and round-down
Alongside the standard "round half up" result, the tool shows the ceiling (always up) and floor (always down) at the same precision. That matters when you can't round down — you need 3.2 boxes, so you buy 4 — or can't round up, like fitting items within a budget.
The half-way rule
When a digit is exactly 5, the common convention is "round half up" (2.5 → 3), which this tool uses. Banking and statistics sometimes use "round half to even" (banker's rounding: 2.5 → 2, 3.5 → 4) to avoid bias across many values, but for everyday work round-half-up is standard.
Where it helps
Reporting a measurement to the right precision, tidying a price, snapping a value to a grid, or figuring out how many whole units you need. For percentage results, round after the calculation, not before, to avoid compounding errors.
Worked example
Take 3.14159. Rounded to 2 decimal places it's 3.14 (the next digit, 1, is below 5). To 3 significant figures it's 3.14 as well, but 3141.59 to 3 significant figures is 3140. And 3.14159 to the nearest 0.5 is 3.0. The round-up of 3.14159 to 2 decimals is 3.15 and the round-down is 3.14 — handy when the direction is forced by context.
Frequently asked questions
What is the difference between decimal places and significant figures?+
Decimal places count digits after the point; significant figures count meaningful digits from the first non-zero one. 0.004567 to 2 decimals is 0.00, but to 2 significant figures is 0.0046.
How do I round to the nearest 10 or 5?+
Use "Nearest multiple" mode and set the precision to 10, 5, 0.5 or any step. The number snaps to the closest multiple: 47 to the nearest 10 is 50.
How does rounding handle a 5?+
This tool uses "round half up": a trailing 5 rounds the previous digit upward, so 2.5 becomes 3 and 2.45 becomes 2.5. It is the most common everyday convention.
What are round-up and round-down?+
Round-up (ceiling) always goes to the higher value at that precision and round-down (floor) always to the lower. Use ceiling when you can’t have less (buying whole boxes) and floor when you can’t exceed a limit.
Should I round before or after calculating?+
Always round at the end. Rounding intermediate values compounds the error; keep full precision through the calculation and round only the final result.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
Spotted a wrong result? Use the "Report a bug" button at the top of the page; every report is reviewed.
How we calculate and our accuracy policy →
Results are for information only. For official matters the relevant authority's calculation prevails.
Last updated: