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Rounding Calculator

Round exact decimal text with five clearly defined modes, without binary floating-point surprises.

Privacy: your files never leave your device. All processing happens locally in your browser.

How to use

  1. 1.Enter a plain decimal number without commas or scientific notation.
  2. 2.Choose a decimal-place count from 0 to 20 and select the required rounding mode.
  3. 3.Select Round number, then copy or compare the exact formatted result.

About Rounding Calculator

Rounding Calculator gives you explicit control over how a decimal value is shortened. Enter a plain decimal, choose from zero through twenty decimal places, and select one of five named modes: half up, half even, floor, ceiling, or truncate. The result preserves the requested number of decimal places, including trailing zeroes, so an answer such as 1000.00 communicates different precision from 1000. This makes the calculator useful for checking worksheets, preparing tabular data, comparing software output, formatting measurements, or understanding why two systems produce different rounded values. All calculation happens locally in the browser, and the number you enter is not uploaded to Lizely.

Unlike a shortcut based on JavaScript's ordinary binary Number type, this calculator processes decimal digits as text and performs the final increment with integer arithmetic. That distinction matters for familiar edge cases such as 1.005 rounded to two places. Many binary floating-point values cannot represent their short decimal spelling exactly, so multiplying and calling a built-in rounding function can produce an unexpected 1.00. Here, the discarded digits are inspected directly. With half up selected, 1.005 becomes 1.01, while 999.999 becomes 1000.00 after the carry crosses the decimal point.

Half up rounds to the nearest result and sends an exact halfway case away from zero. For example, 1.235 becomes 1.24 at two places, and -1.235 becomes -1.24. Half even also rounds to the nearest result, but an exact tie chooses the result whose last retained digit is even. Therefore 2.5 becomes 2 while 3.5 becomes 4 at zero places. Half even can reduce a persistent upward bias when many independently rounded ties are combined, which is why it is often called banker's rounding. The name does not mean it is automatically the correct policy for every financial, legal, scientific, or reporting context. Follow the rule required by your own organization or standard.

The three directed modes do not look for the nearest result. Floor moves toward negative infinity, so -1.21 becomes -2 at zero places. Ceiling moves toward positive infinity, so the same input becomes -1. Truncate simply removes discarded digits and therefore moves a nonzero value toward zero; -1.99 becomes -1. These differences are especially important for negative numbers. A common mistake is to treat floor as another name for dropping digits, even though they agree only for positive values. The labels shown beside each mode state its direction to make that distinction visible before you calculate.

The input accepts an optional plus or minus sign, digits, and one decimal point. A leading zero may be omitted, so .5 is valid. Thousands separators and scientific notation are deliberately rejected rather than interpreted silently. Enter 1000.5 instead of 1,000.5, and expand 1e3 to 1000. The calculator accepts at most 200 digits and at most 20 requested decimal places, which keeps very large pasted inputs responsive while covering ordinary precision checks. Leading zeroes are normalized, and a result with zero magnitude is displayed without a negative sign. Extra zeroes are appended when the requested precision is greater than the number of supplied fractional digits.

Rounding changes presentation and may change a value; it does not establish how many digits are genuinely significant. Decimal places are positions after the decimal point, while significant figures count meaningful digits from the first nonzero digit. This tool handles decimal places only. It does not parse currencies, apply cash-rounding increments such as 0.05, convert fractions, propagate measurement uncertainty, choose a tax rule, or guarantee compliance with an external policy. For a sequence of calculations, keep full precision during intermediate steps and round at the stage specified by the applicable method. Repeatedly rounding intermediate values can accumulate a different total from rounding only the final value.

For a dependable check, copy the original decimal exactly, set the required places, and verify the named mode before using the output. Try a nearby value on each side of a tie when comparing another application, because a disagreement may come from its mode, its input representation, or the stage where rounding occurs. The methodology follows the published Unicode and ICU definitions linked below, including the direction of each mode for negative values. Those definitions explain the calculation rule; they do not select a business policy for you.

Methodology & sources

The calculator validates a plain signed decimal with no separators or exponent, retains the requested 0 to 20 fractional digits, and examines the remaining decimal digits. Half-up increments magnitude at a tie or above; half-even increments above a tie or when an exact tie leaves an odd retained integer; floor increments a negative magnitude when any discarded digit is nonzero; ceiling does the same for a positive value; truncate never increments. Integer arithmetic applies any carry, the decimal point is restored, requested trailing zeroes are retained, and negative zero is normalized to zero.

Frequently asked questions

Why does 1.005 round to 1.01 with half up?
The calculator inspects the decimal digits directly, so the discarded 5 is treated as an exact tie. It does not first approximate 1.005 as a binary floating-point number.
What is the difference between half up and half even?
Both choose the nearest result. At an exact tie, half up moves away from zero, while half even chooses the result with an even last retained digit.
Are floor and truncate the same for negative values?
No. Floor moves toward negative infinity, while truncate moves toward zero. At zero places, -1.21 floors to -2 but truncates to -1.
Can I enter scientific notation or comma separators?
No. Expand scientific notation and remove separators first. For example, enter 1000.5 instead of 1.0005e3 or 1,000.5.

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