1. Find the rounding digit
3.1|4159 to the hundredthLocate the digit in the place you are rounding to. In 3.14159, the hundredths digit is 4.
Exact decimal maths, no floating point errors
Rounding Calculator
This rounding calculator rounds any number to the nearest whole number, tenth, hundredth, thousandth, ten, hundred or any multiple you choose. Pick from seven rounding methods, see it on a number line with step-by-step working, or round a whole list at once.
Round numbers online
Rounded list
| # | Original | Rounded | Change |
|---|
How to round
How to Round Numbers Step by Step
Rounding replaces a number with a simpler value that is close to it. The standard method takes three steps.
2. Look one digit right
next digit: 1If the next digit is 5 or more, the rounding digit goes up by one. If it is 4 or less, the rounding digit stays the same.
3. Drop the rest
3.14159 ≈ 3.14Remove every digit after the rounding digit. When rounding to tens, hundreds or more, replace them with zeros instead.
Rounding to a number of digits instead? To keep a set number of meaningful digits, use the significant figures calculator. For very large or small numbers try the scientific notation calculator.
Place values
Rounding to Each Place Value
Here is the number 1,234.5678 rounded to every common place value with the standard method.
| Round to the nearest | Place value | Result |
|---|---|---|
| Thousand | 1,000 | 1,000 |
| Hundred | 100 | 1,200 |
| Ten | 10 | 1,230 |
| Whole number | 1 | 1,235 |
| Tenth | 0.1 | 1,234.6 |
| Hundredth | 0.01 | 1,234.57 |
| Thousandth | 0.001 | 1,234.568 |
Methods
Rounding Methods Compared
The methods only differ for exact halves and for the always-up and always-down options. This table shows how each one handles tricky cases.
| Method | 2.5 | 3.5 | -2.5 | 2.7 | -2.7 |
|---|---|---|---|---|---|
| Standard (half away from zero) | 3 | 4 | -3 | 3 | -3 |
| Banker’s (half to even) | 2 | 4 | -2 | 3 | -3 |
| Half up (toward + infinity) | 3 | 4 | -2 | 3 | -3 |
| Half down (toward zero) | 2 | 3 | -2 | 3 | -3 |
| Ceiling (always up) | 3 | 4 | -2 | 3 | -2 |
| Floor (always down) | 2 | 3 | -3 | 2 | -3 |
| Truncate | 2 | 3 | -2 | 2 | -2 |
Software uses different rules. Excel’s ROUND function rounds halves away from zero, Python’s round() uses banker’s rounding, and JavaScript’s Math.round() rounds halves toward positive infinity, so Math.round(-2.5) gives -2.
Why ours
Why This Rounding Calculator Is Better
Many online rounding tools use computer floating point and quietly get some answers wrong. This one does not.
Exact decimal maths
Numbers are handled as exact decimals, so 1.005 rounds to 1.01 and very long numbers keep every digit.
Visual number line
See the number sitting between its two rounding options, the halfway point and which way it moves.
Step-by-step working
Each answer explains the rounding digit, the next digit and the rule applied, perfect for homework checks.
Seven rounding methods
Standard, banker’s, half up, half down, ceiling, floor and truncation, matching Excel, Python and accounting rules.
Any multiple
Round to the nearest 5, 25, 0.05 for cash, 0.25 for quarters or any custom step, not just place values.
Round a whole list
Paste hundreds of numbers and get every result plus the total rounding error, ready to copy back to a spreadsheet.
Guide
How to Use the Rounding Calculator
Answers update as you type.
- Choose one number or a list
Round a single value with full working, or paste a list to round many at once.
- Enter your number
Type or paste it. Commas, negative signs and e-notation such as 1.2e-5 all work.
- Pick what to round to
Choose a place value from thousands to ten-thousandths, tap a quick choice, or set any multiple.
- Select a method
Standard rounding suits most schoolwork. Use banker’s rounding for finance or to match Python.
- Check and copy
Read the number line and steps, then copy the result or share the link.
Benefits
Who Uses a Rounding Calculator
Rounding shows up everywhere numbers need to be clear, fair or practical.
Students and teachers
Check homework, practise place value and see why each answer rounds the way it does. Pair it with the decimal to fraction calculator.
Accountants and finance
Apply banker’s rounding to avoid bias in large sums, and see exactly how much rounding changes a total.
Shops and cash handling
Round prices to the nearest 0.05 or 0.10 where small coins are no longer used, or tidy prices after a percentage change.
Developers and analysts
Compare how Excel, Python and JavaScript would round a value and get exact answers free of floating point surprises.
FAQ
Rounding FAQ
How do you round to the nearest tenth?
Look at the digit in the hundredths place, the second digit after the decimal point. If it is 5 or more, add one to the tenths digit; if it is 4 or less, leave the tenths digit as it is. Then drop the remaining digits. For example, 3.47 rounds to 3.5 and 3.43 rounds to 3.4.
How do you round to the nearest hundredth?
Look at the thousandths digit, the third digit after the decimal point. If it is 5 or more, round the hundredths digit up; otherwise keep it. For example, 2.678 rounds to 2.68 and 2.674 rounds to 2.67.
How do you round to the nearest whole number?
Look at the first digit after the decimal point. If it is 5 or more, round up to the next whole number; if it is 4 or less, keep the whole number part. For example, 7.5 rounds to 8 and 7.49 rounds to 7.
Do you round up at 5?
With standard rounding, yes: a 5 in the deciding position rounds up, so 4.5 becomes 5. Other methods treat exact halves differently. Banker’s rounding sends halves to the nearest even number, so 4.5 becomes 4 and 5.5 becomes 6.
What is banker’s rounding?
Banker’s rounding, also called round half to even, rounds exact halves to the nearest even number. 2.5 becomes 2 and 3.5 becomes 4. Because halves go up and down equally often, it avoids an upward bias when many values are added, which is why it is used in finance and by Python’s round() function.
How do you round negative numbers?
With standard rounding, negative numbers round the same way as positive ones but away from zero, so -2.5 becomes -3 and -2.4 becomes -2. Some software differs. JavaScript’s Math.round(-2.5) returns -2 because it rounds halves toward positive infinity.
What is the difference between rounding and truncating?
Rounding moves a number to the nearest value at the chosen place. Truncating simply cuts off the extra digits without looking at them, which always moves toward zero. For example, 3.99 rounds to 4 but truncates to 3.
How do you round to the nearest 5 or 10?
Divide the number by 5 or 10, round the result to a whole number, then multiply back. For example, 47 ÷ 5 = 9.4, which rounds to 9, so 47 rounds to 45 to the nearest 5. 48 ÷ 5 = 9.6 rounds to 10, so 48 rounds to 50.
Why does 1.005 round to 1.00 in some programs?
Most programs store decimals in binary floating point, which cannot represent 1.005 exactly and stores it as slightly less, about 1.00499999. JavaScript and Python therefore round it down to 1.00. This calculator uses exact decimal arithmetic, so 1.005 correctly rounds to 1.01.
Round With Confidence
Use the rounding calculator for schoolwork, finance and data, then explore our other free maths tools.
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