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Rounding Calculator

Round numbers to decimal places or significant figures exactly, half up, half even, up or down.

By Nitin Raturi · Last reviewed

Your number

How to use the Rounding Calculator

Round any number to decimal places or significant figures, exactly.

  1. Type the number.
  2. Choose decimal places or significant figures, and how many.
  3. Choose the rounding method.
  4. Read the rounded value and how much it changed.

Good to know

  • Trailing zeros are kept, because they show the precision.
  • Half even is what many scientific and financial standards use.

Rounded as exact decimal digits, so 2.675 really becomes 2.68.

Number

The number to round. It is handled as exact decimal digits, so nothing is lost to computer rounding.

How to fill it in

  • Type digits, such as 2.675, −0.084 or 1,234.5.
  • Scientific notation such as 6.02e23 also works.

Example

2.675 to two decimals is 2.68.

Round to

Round to

Decimal places count digits after the point; significant figures count digits from the first non-zero one.

How to fill it in

  • Decimal places: money and fixed formats.
  • Significant figures: measurements and science.

Example

0.084024 to two significant figures is 0.084.

How many

The number of decimal places or significant figures to keep.

How to fill it in

  • Decimal places: −10 to 20. Negative places round to tens, hundreds and so on.
  • Significant figures: 1 to 30.

Example

1234.5678 to −2 places is 1200.

Method

What to do with the dropped digits, especially an exact half.

How to fill it in

  • Half up: halves move away from zero, as in spreadsheets.
  • Half even: halves go to the even digit, which avoids bias over many values.
  • Up: any dropped digit moves away from zero. Down: just cut the digits.

Example

−2.5 becomes −3 half up and −2 half even; NIST’s 3.450 and 3.550 become 3.4 and 3.6. Rounded up, 0.084024 is 0.085.

Rounded

2.68

2.675 rounded to 2 decimal places, half up (away from zero), is 2.68.

Change
+0.005

Exact base-ten arithmetic on the digits you type; trailing zeros are kept to show the precision.

ChangelogHow we test this calculatorEmbed this calculator

How this calculator works

  1. Step 1Find the place0.01Decimal places or significant figures set where to cut.
  2. Step 2Look at what is dropped…5Below half, above half, or exactly half.
  3. Step 3Apply the method2.68Keep, add one, or go to the even digit.

The calculator keeps your number as exact decimal digits. Many apps store 2.675 as 2.67499999…, so they round it down to 2.67. Here it becomes 2.68, as it should.

Worked example: an uncertainty

NIST GLP 9, Example 2
Rule
keep 2 significant figures
  1. Uncertainty0.084024 mL
  2. Two significant figures0.084 mL
  3. Rounded up (Option C)0.085 mL

NIST’s laboratory guide rounds an uncertainty to two significant figures, and offers a conservative option that always rounds up.

Rounding an exact half

  • Half up−3−2.5 moves away from zero, as spreadsheets do.
  • Half even−2−2.5 goes to the even digit.

Half even avoids an upward bias when many values end in 5. NIST’s examples: 3.450 becomes 3.4 and 3.550 becomes 3.6.

Read the result

The headline is the rounded number, with its trailing zeros; the change line shows exactly how much was added or dropped.

Negative decimal places round to tens, hundreds and beyond: 1234.5678 to −2 places is 1200.

Assumptions and limits

  • Exact digitsUp to 60 digits, with no binary rounding error.
  • Ties definedHalf up moves away from zero; half even goes to the even digit.
  • Zeros kept1.2 to four places is 1.2000.

Rounding is a choice of rule and of precision. Significant figures and notation are related choices.

To count and round by significant figures, use the significant figures calculator. The scientific notation calculator writes very large or small numbers compactly, rounded exactly.

Common mistakes

  • Mistake: Rounding in several steps: 2.445 → 2.45 → 2.5.

    Instead: Round once, from the original number: 2.445 to one place is 2.4.

  • Mistake: Dropping trailing zeros that show precision.

    Instead: Write 2.50 if you measured to two decimals.

  • Mistake: Counting leading zeros as significant.

    Instead: In 0.084, the significant figures start at 8.

Checking the method

Every golden case is rechecked with Python’s exact decimal arithmetic, and NIST’s GLP 9 examples are reproduced.

An independent script uses Python’s decimal module, which rounds in base ten, and compares every result.

Read how we test our calculators, or browse more maths calculators.

Frequently asked questions

What is 2.675 rounded to two decimal places?

2.68. Some apps show 2.67 because they store 2.675 as 2.67499…; this calculator uses exact decimal digits.

What is the difference between half up and half even?

They differ only on an exact half. −2.5 becomes −3 half up and −2 half even.

How do I round to significant figures?

Count from the first non-zero digit. 0.084024 to two significant figures is 0.084.

What does a negative number of decimal places mean?

Rounding to tens (−1), hundreds (−2) and so on. 1234.5678 to −2 places is 1200.

Why are trailing zeros kept?

They show how precise the value is: 1.20 means it was measured to two decimal places.

Sources and methodology

The formulas are standard time-value-of-money results. We check every figure against golden values worked out independently, by closed form and by month-by-month simulation; see the methodology.

Written and maintained by Nitin Raturi, a software engineer (about the author). Last reviewed 3 Nov 2026; next review due by . Found an error? Tell us.

Changelog

  • : Initial release.