Rounding calculator
Round an exact decimal to a chosen number of decimal places, significant figures, or place value, with nine standard tie-breaking modes.
Rounding inputs
The sample is calculated immediately. Replace any value to update the result.
Use a period as the decimal separator. Standard comma grouping and scientific notation are accepted.
Choose how the target precision is defined.
Enter a whole number from 0 to 20.
Select the power-of-ten place that should remain.
Half up is the familiar school rule; other modes change ties or directed rounding.
Live result
All values come from exact base-10 integer arithmetic before display formatting.
Rounded result
3,324.24
3324.238576 rounded to 2 decimal places using half up.
Rounding mode comparison
Compare the same number and target across every supported mode.
| Rounding mode | Rounded result | Adjustment | Rule |
|---|---|---|---|
| Half up | 3,324.24 | +0.001424 | Nearest; ties away from zero |
| Half down | 3,324.24 | +0.001424 | Nearest; ties toward zero |
| Half even | 3,324.24 | +0.001424 | Nearest; ties to an even retained digit |
| Half toward +∞ | 3,324.24 | +0.001424 | Nearest; ties toward positive infinity |
| Half toward – ∞ | 3,324.24 | +0.001424 | Nearest; ties toward negative infinity |
| Away from zero | 3,324.24 | +0.001424 | Any discarded nonzero digit increases magnitude |
| Toward zero | 3,324.23 | – 0.008576 | Discard digits without increasing magnitude |
| Ceiling | 3,324.24 | +0.001424 | Round toward positive infinity |
| Floor | 3,324.23 | – 0.008576 | Round toward negative infinity |
For this sample, the next discarded digit is 8, so all nearest modes agree. Directed modes can still differ.
How to use this rounding calculator
What this calculator does
This calculator reduces the precision of one finite decimal number. It can round by a fixed count of decimal places, by significant figures, or by a named power-of-ten place value. It also lets you choose how exact halfway cases and directed rounding behave. The tool reports the rounded result, the signed adjustment, the absolute error, and the direction of change. It does not determine how much precision your measurement, financial record, or scientific result ought to have; that decision depends on the source data and the rules of your field.
When to use it
Use it when preparing a value for a report, converting a long calculation to a practical display precision, checking how a negative tie behaves, or comparing half-even accounting-style rounding with the familiar half-up rule. It is also useful for classroom exercises involving tenths, hundredths, thousands, or significant figures.
How to calculate
- The calculator opens with the demonstration number 3324.238576, a target of 2 decimal places, and Half up. Its workbook is already validated, so Download Excel is available immediately.
- Replace Number with the decimal you want to round. Then choose Round to. For Decimal places or Significant figures, enter the whole-number Decimal places or Significant figures count. For Place value, choose the named Place value.
- Select a Rounding mode. Read the live Rounded result first, then use Adjustment, Absolute error, and Direction to understand the change. The Rounding mode comparison table shows how the same inputs behave under all nine rules.
- Choose Download Excel to export the current canonical inputs, outputs, and comparison rows. Reset clears the demonstration data rather than restoring it. After Reset, Download Excel is disabled until a complete valid state is entered again.
Input guide
Number is required. Enter a finite base-10 number with no more than 15 significant digits. A period is the decimal separator; commas are allowed only as standard three-digit grouping, such as 12,345.67. Scientific notation such as 1.25e3 is accepted. Unsupported symbols, ambiguous decimal commas such as 1,5, and nonfinite terms are rejected. A larger or smaller number changes the scale and may change which digit is retained.
Round to is required and has three options. Decimal places counts digits to the right of the decimal point. Significant figures counts meaningful digits from the first nonzero digit. Place value keeps a named place such as the nearest hundred or nearest thousandth. Do not confuse two decimal places with two significant figures: 0.012345 becomes 0.01 at two decimal places but 0.012 at two significant figures.
Decimal places accepts a required whole number from 0 to 20. For example, 2 means hundredths. When Round to is Significant figures, the same control is relabeled Significant figures and accepts 1 to 15; for example, 3 keeps three meaningful digits. Place value appears only for the Place value method and ranges from nearest million through nearest millionth. Choosing a coarser place usually increases the possible absolute error.
Rounding mode is required. Half up chooses the nearest value and sends exact ties away from zero. Half down sends ties toward zero. Half even sends ties to the candidate with an even retained digit. Half toward +∞ and Half toward – ∞ resolve ties by direction. Away from zero, Toward zero, Ceiling, and Floor are directed modes and react to any discarded nonzero digit. Python's authoritative decimal rounding-mode documentation provides a useful technical comparison of equivalent rules.
Output guide
Rounded result is the selected approximation and is an exact identity under the chosen rule. Original number is the normalized input. Adjustment equals rounded result minus original number; positive means the result moved upward on the number line, negative means downward, and zero means the input was already at the target precision. Absolute error is the nonnegative magnitude of that adjustment. Direction summarizes it as Up, Down, or Unchanged. The Target, Mode, and Direction summary pills repeat the current canonical state.
In the Rounding mode comparison table, the Rounding mode column names the rule, Rounded result shows that rule's output, Adjustment shows its signed change, and Rule explains its treatment of discarded digits or ties. A high absolute error is not automatically wrong; it means the target is coarse relative to the original value. A zero absolute error means rounding did not alter the number.
Worked example
The startup example rounds 3324.238576 to two decimal places with Half up. Keeping the hundredths gives 3324.23, and the next digit is 8. Because 8 is greater than 5, the retained hundredths digit increases from 3 to 4. The exact displayed result is 3,324.24. The signed adjustment is +0.001424, calculated as 3324.24 – 3324.238576, and the absolute error is 0.001424. The direction is therefore Up.
How the rounding rule works
Every target can be expressed as a power-of-ten step. Two decimal places use a step of 0.01; the nearest hundred uses a step of 100. The calculator divides the exact decimal by that step, examines the whole quotient and discarded remainder, applies the selected mode, and multiplies back by the same step. Internally it uses integer coefficients and decimal scales, avoiding the binary floating-point surprise that can occur with values such as 2.675.
For measurements and published quantities, the target precision should reflect the quality of the source data. The NIST Guide to expressing values of quantities discusses conventions for reporting numerical values and uncertainty. For software behavior, note that a language's built-in rounding function may implement only one tie rule; for example, MDN's Math.round reference documents JavaScript's specific behavior.
Common rounding mistakes
- Rounding intermediate steps: repeated rounding can compound error. Keep full precision through the calculation and round the final result unless a governing rule says otherwise.
- Mixing significant figures and decimal places: they coincide only for some values. Significant figures move with the magnitude of the number.
- Ignoring negative-number direction: Floor moves toward negative infinity, while Toward zero removes magnitude. For – 3.2, those results are – 4 and – 3.
- Assuming every tie goes upward: half-even, half-down, half-ceiling, and half-floor deliberately resolve exact halves differently.
- Claiming false precision: extra trailing digits can imply accuracy the original measurement never had.