A precise rounding calculator for decimals, sig figs and multiples
This rounding calculator rounds any number to a chosen number of decimal places, significant figures or the nearest multiple — 10, 100, 1,000, 0.5, 0.25 or any value you type. Pick from seven rounding modes, including the school-standard half up, banker’s rounding (half even), ceiling, floor and truncation, and see why the answer came out that way.
Unlike many calculators and spreadsheets, it works on the decimal digits you typed rather than on a binary approximation. That is why 1.005 correctly rounds to 1.01 here, while plenty of software returns 1.00. It handles hundreds of digits, negatives and e-notation, and compares every mode side by side.
How to use the Rounding Calculator
- Type the number you want to round. Commas and spaces are ignored, and e-notation such as 4.5e-7 works too.
- Choose what to round to: decimal places, significant figures or the nearest multiple.
- Set the precision — for example 2 decimal places, 3 significant figures, or “nearest 0.25”.
- Pick a rounding mode. Half up is the method taught in most schools; half even is common in finance and statistics.
- Read the result, the explanation of the discarded part and the rounding error, then compare every mode in the table.
Rounding Calculator features
Exact decimal arithmetic
Numbers are rounded digit by digit using big-integer maths, so there are no binary floating-point errors.
Seven rounding modes
Half up, half down, half even, half away from zero, ceiling, floor and truncate — clearly defined for negative numbers too.
Significant figures with sci notation
Sig-fig results also appear in scientific notation, so 120000 to 2 s.f. is unambiguous as 1.2 × 10⁵.
Any multiple
Round prices to 0.05, times to 15 minutes or quantities to packs of 12.
Explains the decision
See the rounding step, the digits kept, the part thrown away and whether it was a tie.
Every mode compared
A table shows how your number rounds in all seven modes, with the change each one makes.
Rounding modes explained
All the “half” modes agree whenever the discarded part is clearly more or less than half a step: 2.4 rounds to 2 and 2.6 rounds to 3. They differ only on ties — numbers exactly halfway, such as 2.5 or −2.5. Half up sends ties toward positive infinity, so 2.5 becomes 3 but −2.5 becomes −2. Half away from zero treats the size of the number symmetrically, so −2.5 becomes −3; this is what Excel’s ROUND does and what most people mean by “normal” rounding. Half even, also called banker’s rounding, sends a tie to whichever neighbour is even (2.5 → 2, 3.5 → 4), which avoids an upward bias when many values are rounded and added up.
The directed modes ignore halfway altogether. Ceiling always rounds toward +∞, floor always toward −∞, and truncate simply chops off the extra digits, moving toward zero.
| Number | Half up | Half down | Half even | Half away from 0 | Ceiling | Floor | Truncate |
|---|---|---|---|---|---|---|---|
| 2.5 | 3 | 2 | 2 | 3 | 3 | 2 | 2 |
| 3.5 | 4 | 3 | 4 | 4 | 4 | 3 | 3 |
| −2.5 | −2 | −3 | −2 | −3 | −2 | −3 | −2 |
| 2.4 | 2 | 2 | 2 | 2 | 3 | 2 | 2 |
| −2.6 | −3 | −3 | −3 | −3 | −2 | −3 | −2 |
Decimal places vs significant figures
Decimal places count digits after the decimal point, regardless of how big the number is: 3.14159 to 2 d.p. is 3.14, and 1,234.5678 to 2 d.p. is 1,234.57. Use them for money (2 d.p. for dollars, pounds, euros and rupees) and fixed-precision measurements.
Significant figures count meaningful digits starting from the first non-zero digit, so they keep the same relative precision for any size of number: 0.0004567 to 2 s.f. is 0.00046, and 123,456 to 2 s.f. is 120,000. Leading zeros are never significant; trailing zeros after a decimal point are, which is why 9.996 to 3 s.f. is written 10.0, not 10. To count sig figs digit by digit or apply them to + − × ÷, use the significant figures calculator; the scientific notation converter rewrites them in powers of ten.
Why 1.005 rounds to 1.00 in so many programs
Most software stores numbers in binary floating point, which cannot represent 1.005 exactly. The stored value is about 1.00499999999999989, which is just under the halfway point, so a naive “multiply by 100, round, divide by 100” returns 1.00. The same thing happens with 2.675 (stored as 2.67499999…) and many other values. This calculator never converts your number to binary, so it always rounds the number you actually typed. When a common floating-point shortcut would give a different answer, a note under the result tells you so.
Rounding to the nearest 10, 100, 0.5 or any multiple
- Nearest 10 or 100: 1,234 rounds to 1,230 (nearest 10) and 1,200 (nearest 100). For estimating sums, this is the quickest mental-maths trick.
- Nearest 0.5: common for grades, shoe sizes and ratings — 7.3 becomes 7.5 and 7.2 becomes 7.0.
- Nearest 0.05: cash rounding in countries without 1-cent coins.
- Custom multiples: 52 minutes to the nearest 15 is 45 minutes; with ceiling it is 60, which is how many services bill time.
Rounding Calculator FAQ
How do I round to 2 decimal places?
Look at the third digit after the decimal point. If it is 5 or more, increase the second digit by one; otherwise leave it. So 3.14159 becomes 3.14 and 2.675 becomes 2.68. Choose “Decimal places”, enter 2 and the rounding calculator does it for you.
What is banker’s rounding?
Banker’s rounding (round half to even) rounds exact halves to the nearest even digit: 2.5 → 2, 3.5 → 4, 0.125 → 0.12 at 2 d.p. It is used in finance, statistics and IEEE 754 arithmetic because it does not push totals upward on average.
How do I round −2.5?
It depends on the mode. Half away from zero (Excel’s ROUND and the usual school rule) gives −3. Half up, which sends ties toward positive infinity, gives −2. Half even also gives −2, because 2 is even.
How many significant figures does 0.00450 have?
Three: 4, 5 and the final 0. Leading zeros only locate the decimal point, but a trailing zero after the decimal point shows the measurement was precise to that digit.
What is the difference between truncating and rounding down?
For positive numbers they are the same. For negative numbers, truncating moves toward zero (−3.79 → −3.7) while rounding down (floor) moves toward negative infinity (−3.79 → −3.8).
Why does my spreadsheet give a different answer?
Usually because of binary floating-point storage (1.005 is stored as 1.00499999…) or because it uses a different tie rule. Compare all seven modes here to see which rule your software follows.