What this calculator does
Round any number the way you need it, and see exactly how the answer was reached. Rounding swaps a number for a nearby, simpler one. Think of a price to the nearest cent, or a measurement to what your ruler can show. Or think of a count rounded to the nearest box of five. This calculator handles all three: decimal places, significant figures, and the nearest multiple of any step you choose.
The tricky part is a number that sits exactly halfway between two choices. Different fields use different rules for that. So the calculator lets you pick a rule, and it also shows what each of the four common rules would give, side by side.
Where it's used
Why this math matters outside the classroom:
- Shopping estimates. Shoppers round a $19.96 item to $20 to estimate the total of their cart quickly.
- Race times. A sprinter's time of 12.347 seconds is posted as 12.35 when rounded to hundredths.
- Population figures. News reports round a city population of 508,394 to about 508,000, to the nearest thousand.
- Ordering supplies. A builder who needs 37 boards sold in bundles of 10 rounds up to the next multiple, 40.
- Banker's rounding. Accountants who round half to even turn 2.345 into 2.34 and 2.355 into 2.36, which avoids an upward bias.
Grade level and standards: Grades 4–5; Common Core State Standards for Mathematics 5.NBT.A.4, 4.NBT.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter the number you want to round. Negative numbers, long decimals and exponent form such as 1.5e-7 all work.
- Choose what to round to: a number of decimal places, a number of significant figures, or the nearest multiple of a step such as 5, 10 or 0.25.
- Pick a rounding method. Half up is the everyday rule from school. Half to even is common in finance and statistics. Always up and always down are also called the ceiling and the floor.
- Read the rounded number, the version written with its trailing zeros, and the table comparing every method.
What the inputs mean
- Number to round
- Rounding works on the number exactly as you typed it. So 1.005 is treated as exactly 1.005, not the slightly smaller value a computer stores in binary.
- Significant figures
- Significant figures are the digits that carry meaning, counted from the first digit that isn't zero. 0.004567 to two significant figures is 0.0046. The zeros at the front only show where the decimal point sits.
- Multiple
- Any positive step. Use 5 or 10 for whole-number groups, 0.25 for quarters, or 0.05 for rounding cash to the nearest nickel.
- Rounding method
- Half up and half to even only differ on exact ties. Always up moves toward the bigger numbers (positive infinity). Always down moves toward the smaller ones (negative infinity). So for negative numbers, −2.5 rounds up to −2 and down to −3.
Formula and method
unit = 10^(−d) for d decimal places unit = 10^(e − s + 1) for s significant figures, where e is the place of the first nonzero digit unit = m for the nearest multiple of m count = x ÷ unit, round the count to a whole number, rounded value = count × unit
In the formulas, x is your number and the unit is the size of step you're rounding to. The letter d is the number of decimal places, s is the number of significant figures, and m is the multiple. The letter e is the place of the first digit that isn't zero, written as a power of 10.
Every kind of rounding is really the same job. Pick a unit, count how many of those units fit in your number, round that count to a whole number, and multiply back. Rounding 1234.5678 to two decimal places uses a unit of 0.01. To three significant figures, it uses a unit of 10. To the nearest five, it uses 5.
The method only decides how the count becomes a whole number. Half up sends an exact .5 away from zero. Half to even sends it to whichever neighbour is even, so over many numbers, ties go up as often as down. The ceiling always moves toward the bigger numbers unless the count is already whole. The floor always moves toward the smaller numbers.
Worked example
Round 2.665 to two decimal places with each method.
- Two decimal places means a unit of 0.01. And 2.665 ÷ 0.01 = 266.5 units, an exact tie.
- Half up sends the tie away from zero: 267 units, so 2.67.
- Half to even picks the even neighbour, 266, so 2.66.
- Always up gives 267 units (2.67) and always down gives 266 units (2.66).
Result: 2.665 rounds to 2.67 with half up or always up, and to 2.66 with half to even or always down.
Understanding the result
The rounded number stands in for the original; it doesn't correct it. Keep every digit while you work, and round once at the end. If you round at every step along the way, small errors can pile up.
The "written with trailing zeros" result keeps zeros that carry meaning. 2.5 rounded to three significant figures is written 2.50. That tells a reader the hundredths digit was measured, and it's zero.
If the comparison table shows the same answer for every method, your number wasn't on a tie. The choice of rule didn't matter, apart from which way the ceiling and floor go.
Assumptions and limitations
- Your number is read as the shortest decimal that matches what you entered. Every rounding choice is then made exactly in decimal. So typed halves such as 1.005 or 0.125 are treated as true ties.
- Half up means half away from zero, so −2.5 becomes −3. Some spreadsheets use "round half up" to mean toward the bigger numbers (positive infinity) instead. That version isn't offered here.
- Numbers are limited to about 15–17 significant digits, which is how precisely a computer normally stores a number (a "double"). Digits typed beyond that are lost before rounding begins.
- With significant figures, zeros at the end of a whole number such as 1230 are unclear on their own. If the count of significant figures matters, write the result in scientific notation (1.23 × 10³).
Frequently asked questions
Why does my spreadsheet or code round 1.005 to 1.00?
Computers store 1.005 in binary as about 1.00499999999999989. That's just below the halfway point, so a basic rounding routine goes down. This calculator works on the decimal digits you typed. So 1.005 is a true tie, and half up rounds it to 1.01.
What is banker's rounding and when should I use it?
Banker's rounding is the half-to-even rule. An exact half goes to the even neighbour, so 2.5 becomes 2 and 3.5 becomes 4. Ties go up and down equally often, so a total of many rounded numbers doesn't creep upward. It's the default in many accounting and statistics tools.
How do I round to the nearest 5, 10 or quarter?
Choose "Nearest multiple" and enter the step. 37 to the nearest 5 is 35, 3.38 to the nearest 0.25 is 3.5, and 1,234 to the nearest 100 is 1,200. The same four methods apply, so you can also always round up to the next multiple.
How do significant figures differ from decimal places?
Decimal places count the digits after the decimal point, however big the number is. Significant figures count from the first digit that isn't zero. That keeps the same precision relative to the number's size. For example, 0.004567 and 4567 round to two significant figures as 0.0046 and 4600.
Does rounding up a negative number make it bigger or smaller?
Here, always up means toward the bigger numbers (positive infinity). So a negative number moves toward zero and gets larger: −2.7 rounds up to −2. Always down moves toward the smaller numbers (negative infinity): −2.1 rounds down to −3.
How this calculator is checked
Method: Standard rounding rules (round half away from zero, round half to even, ceiling, floor) applied in exact decimal arithmetic. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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