Quick answer
Rounding to d decimal places is round(x × 10^d) ÷ 10^d. 3.14159 rounded to 2 places is 3.14, a difference of −0.00159.
Enter a number, the decimal places and the rounding mode. The calculator returns the rounded value and the difference.
Related tools: Fraction Calculator: Add, subtract, multiply and divide fractions with simplified and mixed-number results. Ratio Calculator: Simplify a ratio of two whole numbers. Average Calculator: Arithmetic mean, sum, count, minimum and maximum of a list of numbers.
How to use the Rounding Calculator
- Enter number.
- Enter decimal places (a whole number, between -9 and 12). It starts at 2.
- Choose mode: Nearest (half away from zero), Up (toward +∞) and Down (toward −∞).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Number | A number | — |
| Decimal places | A whole number | ≥ -9, ≤ 12, starts at 2 |
| Mode | Choose one: Nearest (half away from zero); Up (toward +∞); Down (toward −∞) | Starts at Nearest (half away from zero) |
Formula and method
Formula
round(x × 10ᵈ) ÷ 10ᵈ
IEEE-754 double precision; shown to at most 6 decimal places.
Negative decimal places round to tens, hundreds and so on. Nearest rounds exact halves away from zero.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Number = 3.14159; Decimal places = 2; Mode = Nearest (half away from zero).
| Result | Value |
|---|---|
| Rounded | 3.14 |
| Difference | -0.00159 |
Example 2
Inputs: Number = 2.5; Decimal places = 0; Mode = Nearest (half away from zero).
| Result | Value |
|---|---|
| Rounded | 3 |
| Difference | 0.5 |
Example 3
Inputs: Number = -2.5; Decimal places = 0; Mode = Nearest (half away from zero).
| Result | Value |
|---|---|
| Rounded | -3 |
| Difference | -0.5 |
The first line is the headline result (rounded). Below it the rounding Calculator lists difference, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Rounding modes
Nearest rounds exact halves away from zero, so 2.5 becomes 3 and −2.5 becomes −3. Up rounds toward +∞ (2.1 becomes 3, −2.9 becomes −2) and down rounds toward −∞ (2.9 becomes 2, −2.1 becomes −3). Banker's rounding (half to even), which sends 2.5 to 2, is used in some software but is not offered here.
Floating-point limits
Computers store most decimals in binary, so a value such as 1.005 is actually slightly below 1.005 and may round to 1 rather than 1.01. Rounding to a stated precision after a long calculation is better than rounding at each step.
How the result changes with number
Holding every other input at the first worked example, this table changes only number. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Number | Rounded | Difference |
|---|---|---|
| 1.571 | 1.57 | -0.001 |
| 3.142 | 3.14 | -0.002 |
| 6.283 | 6.28 | -0.003 |
| 12.57 | 12.57 | 0 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Number: entering "a" shows "Number must be a number." beside that field and no result.
Choosing between the Rounding Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
| [Ratio Calculator](/math/ratio-calculator/) | first number and second number | Simplified ratio |
| [Average Calculator](/math/average-calculator/) | numbers | Average (mean) |
| [Long Division Calculator](/math/long-division-calculator/) | dividend and divisor | Quotient |
| [Percent Off Calculator](/math/percent-off-calculator/) | original price and discount | Sale price |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Binary floating point cannot represent some decimal halves exactly
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for number to confirm this.
Frequently asked questions
How do I round to the nearest 10?
Use a negative number of decimal places, for example −1.
What is 2.5 rounded?
3 in the nearest mode, because exact halves go away from zero.
What is significant-figure rounding?
A different method, which counts digits rather than decimal places.
What does the Rounding Calculator calculate?
Round a number to decimal places, with up, down or nearest modes. It returns Rounded and Difference.
What formula does the Rounding Calculator use?
round(x × 10ᵈ) ÷ 10ᵈ. Negative decimal places round to tens, hundreds and so on.
What do I need to enter in the rounding Calculator?
You enter Number, Decimal places and Mode.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Binary floating point cannot represent some decimal halves exactly.
What does the “Mode” option change?
It sets how the rounding is worked out. The choices are Nearest (half away from zero), Up (toward +∞) and Down (toward −∞).
What is an example of a rounding result?
With number 3.14159, decimal places 2 and mode Nearest (half away from zero), the rounded is 3.14.
Where does the method come from?
The method follows: IEEE 754 rounding terminology.
Related calculators
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Ratio Calculator — Simplify a ratio of two whole numbers.
- Average Calculator — Arithmetic mean, sum, count, minimum and maximum of a list of numbers.
- Long Division Calculator — Divide whole numbers to a chosen number of decimal places.
- Percent Off Calculator — Find the sale price and savings after a percentage discount.
- Percent Error Calculator — Compare a measured value with the true value.
Sources
- IEEE 754 rounding terminology
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.