Home › Math › Rounding Calculator

Rounding Calculator

Rounds a number to a given number of decimal places (negative for tens, hundreds, …) or significant figures using round-half-away-from-zero, and also reports the ceiling, floor and truncated values at the same precision.

When to use

You need a number rounded to a fixed number of decimals or significant figures, or its ceiling/floor at that precision, with the exact decimal behaviour (2.675 → 2.68).

Do not use when: You want a number written in scientific or engineering notation (use scientific-notation).

Formula

rounded = round_half_away(value × 10^p) / 10^p, where p = precision (decimals) or p = precision − 1 − ⌊log10|value|⌋ (significant figures); ceiling, floor and truncated use ⌈·⌉, ⌊·⌋ and trunc(·) instead

The decimal shift uses the exact decimal digits of the input, so ties such as 2.675 are recognised as ties and rounded away from zero (2.68) instead of following binary floating-point noise (2.67).

Inputs

Parameter	Type	Required	Description
`value`	number	yes	The number to round. Range: ≥ -1000000000000, ≤ 1000000000000
`precision`	integer	default 2	Decimal places when mode is decimals (negative rounds to tens, hundreds, …), or the number of significant figures (1–12) when mode is significant_figures. Range: ≥ -9, ≤ 12
`mode`	enum: decimals \| significant_figures	default decimals	Whether precision counts decimal places or significant figures.

Outputs

Output	Type	Description
`rounded`	number	Value rounded half away from zero at the requested precision.
`rounded_text`	string	The rounded value written with the requested number of decimals, e.g. '2.68' or '12300'.
`ceiling`	number	Smallest value at that precision that is ≥ value.
`floor`	number	Largest value at that precision that is ≤ value.
`truncated`	number	Value with the extra digits dropped (rounded toward zero).
`decimal_places_used`	integer	The decimal-place count actually used (derived from the magnitude in significant-figure mode).

Example

2.675 to 2 decimals: {"value":2.675,"precision":2,"mode":"decimals"} → {"rounded":2.68,"rounded_text":"2.68","ceiling":2.68,"floor":2.67,"truncated":2.67,"decimal_places_used":2}

12345.678 to 3 significant figures: {"value":12345.678,"precision":3,"mode":"significant_figures"} → {"rounded":12300,"rounded_text":"12300","ceiling":12400,"floor":12300,"truncated":12300,"decimal_places_used":-2}

GET https://tttkmbb.com/api/v1/calculate/rounding?value=2.675&precision=2&mode=decimals

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/rounding (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/rounding · Markdown: https://tttkmbb.com/math/rounding.md · JSON definition: https://tttkmbb.com/math/rounding.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="rounding"
OpenAPI operationId: calculate_rounded_value
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Rounding (reference)
Wikipedia – Significant figures (reference)
Wolfram MathWorld – Significant Digits (reference)

FAQ

Which tie-breaking rule is used?

Round half away from zero: 2.5 → 3, −2.5 → −3, 2.675 → 2.68. Spreadsheets use the same rule; Python's round() and IEEE 754 default to round-half-to-even, which gives 2 for 2.5.

How do I round to the nearest hundred?

Use mode decimals with precision −2: 12345.678 → 12300.

Related calculators

Scientific Notation Converter — Write the rounded number in scientific or engineering form.
Percentage Calculator — Percent results that usually need rounding.