Rounding Calculator
Round to any decimal place, to tens or thousands, or to N significant figures — half-up, banker's, floor, ceiling or truncate — with the rule explained.
Rounding Calculator: with the default inputs, rounded is 3.14.
Used only when rounding to N significant figures.
- As a number
- 3.14The same value; trailing zeros are dropped here.
- In scientific notation
- 3.14 × 10⁰Shows exactly which digits are significant.
- Rounding error (rounded − original)
- -0.00159
- Relative error
- 0.050611%
Assumptions
- Rounding operates on the decimal digits of the number as typed (its shortest exact representation), not on its binary approximation.
- 'Round half up' means half away from zero, matching most school textbooks and Excel.
| Rule | Result |
|---|---|
| Round half up (away from zero) — schoolbook | 3.14 |
| Round half to even — banker's rounding | 3.14 |
| Floor (always round down, toward −∞) | 3.14 |
| Ceiling (always round up, toward +∞) | 3.15 |
| Truncate (chop digits off, toward zero) | 3.14 |
| Round to | Result |
|---|---|
| Nearest whole number | 3 |
| Nearest tenth (1 decimal) | 3.1 |
| Nearest hundredth (2 decimals) | 3.14 |
| Nearest thousandth (3 decimals) | 3.142 |
| Nearest ten | 0 |
| Nearest hundred | 0 |
| Nearest thousand | 0 |
How this is worked out
The formula
Round half up (away from zero): look at the next digit — 5 or more rounds up, 4 or less keeps Round half to even: same, except an exact half (…5000) rounds to the even neighbour Floor: toward −∞ Ceiling: toward +∞ Truncate: toward 0 N significant figures: keep N digits counting from the first non-zero digit
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Number
- A number.defaults to 3.14159
- Round to
- Choose one of 8 options.Nearest whole number · Nearest tenth (1 decimal) · Nearest hundredth (2 decimals) · Nearest thousandth (3 decimals) · Nearest ten · Nearest hundred · Nearest thousand · N significant figures
- Significant figures
- Used only when rounding to N significant figures.from 1 to 15 · whole numbers only · defaults to 3
- Rounding rule
- Choose one of 5 options.Round half up (away from zero) — schoolbook · Round half to even — banker's rounding · Floor (always round down, toward −∞) · Ceiling (always round up, toward +∞) · Truncate (chop digits off, toward zero)
What you get back
- Roundedmain answer
- As a number
- The same value; trailing zeros are dropped here.
- In scientific notation
- Shows exactly which digits are significant.
- Rounding error (rounded − original)
- Relative error
What this assumes
- Rounding operates on the decimal digits of the number as typed (its shortest exact representation), not on its binary approximation.
- 'Round half up' means half away from zero, matching most school textbooks and Excel.
About this calculator
Rounding replaces a number with a nearby simpler one. Simple — except that "nearby" has several definitions, they disagree exactly on the halves, and computers add float noise on top. This calculator does the arithmetic on the decimal digits you typed, so 1.005 rounds to 1.01 the way a person expects, not to 1.00 because of binary representation, and it keeps trailing zeros (2.50, not 2.5) because they carry meaning.
How to use it
Enter the number, pick the place to round to (or a count of significant figures) and choose the rule. The steps name the digit at the rounding position, the digit after it, and why the rule went up or down. The tables show what every rule gives at your precision, and what your rule gives at every common precision, so you can see exactly where they differ.
The rules
- Round half up (away from zero) is what schools teach: 5 or more goes up. Strictly it rounds away from zero, so −2.5 becomes −3. Excel's ROUND does this.
- Round half to even (banker's rounding) sends exact halves to the even neighbour: 2.5 → 2, 3.5 → 4. Over many numbers the ups and downs cancel, so sums don't drift upward. It's the IEEE 754 default, and Python's round() uses it.
- Floor always goes down (toward −∞), ceiling always up. Useful for "how many boxes do I need" (ceiling) and "how many full hours" (floor).
- Truncate just chops digits, so it's like floor for positives and ceiling for negatives.
The rules only differ when there's a tie (exactly half) or when the number is negative. For 3.14159 they all agree except ceiling.
Significant figures
Decimal places count from the point; significant figures count from the first non-zero digit. 0.004567 to 2 significant figures is 0.0046 (that's 4 decimal places); 4567 to 2 significant figures is 4600. When the result is something like 4600 the trailing zeros are ambiguous, so the calculator also shows 4.6 × 10³, which is unambiguous.
Common mistakes
- Rounding in stages: 2.4449 → 2.445 → 2.45 → 2.5 is wrong. Look only at the digit immediately after the rounding position — 2.4449 to one decimal is 2.4.
- Dropping meaningful zeros. 2.50 says "accurate to hundredths"; 2.5 doesn't.
- Expecting −2.5 to round to −2 under "half up". Away-from-zero gives −3; if you want −2 you want ceiling or half-to-even.
Frequently asked questions
▸How do I round to the nearest hundredth?
Keep two digits after the decimal point and look at the third: 5 or more rounds the second digit up, otherwise leave it. 3.14159 → 3.14; 2.675 → 2.68.
▸What is banker's rounding?
Round half to even: exact halves go to the nearest even digit, so 2.5 → 2 and 3.5 → 4. Everything else rounds normally. It avoids the upward bias of always rounding halves up.
▸Why does my spreadsheet or Python round 2.675 to 2.67?
Because 2.675 can't be stored exactly in binary — it's really 2.67499999…, which is below the half. This calculator rounds the decimal digits you typed, so it gives 2.68.
▸How are significant figures different from decimal places?
Decimal places count digits after the point; significant figures count digits starting from the first non-zero one. 0.0123 has 4 decimal places but 3 significant figures.
▸Does rounding −2.5 give −2 or −3?
Depends on the rule. Half away from zero gives −3, half to even gives −2, floor gives −3, ceiling gives −2, truncate gives −2. Pick the rule that matches your context.
Put this calculator on your own site
A working rounding, free for any site, with no ads and no sign-up. It resizes to fit wherever you paste it and updates itself as this page improves.
Paste this anywhere. It works on any site, carries no ads, never expires, and always shows the current version.
Rounding Calculator by CalculateItNow
The page's own title. The clearest description of what the link leads to.
The credit line sits outside the widget on purpose, so it is a real link on your page rather than one buried in a frame. Please keep it — it is what pays for CalculateItNow staying free and ad-free. The script only resizes the widget to fit its contents; drop it and the widget still works.
Browse every calculator widget·How to add it to WordPress, Squarespace or Wix
Related calculators
The questions people ask next to a rounding.
Convert any number to scientific, engineering and E notation with chosen significant figures, or expand a × 10ⁿ back to a plain decimal — exactly, no float noise.
a mod b with the quotient and remainder, showing where the mathematical modulo and the % operator in C, Java and JavaScript disagree on negative numbers.
Find what percent one number is of another, take a percentage of a number, or calculate percentage increase and decrease — with the working shown.
Find the mean, median, mode, sum and range of up to 10 numbers, with the work shown and a deviation table that explains what the mean really is.
Add, subtract, multiply and divide fractions and mixed numbers — exact simplified answers with the common denominator and every step shown.