What is the difference between rounding and truncation?

Rounding adjusts the last digit based on the next digit (up if ≥ 5). Truncation simply drops all digits beyond the desired precision without adjustment.

What does 'round to the nearest 10' mean?

Replace the units digit with 0, rounding up if the units digit is 5 or more. 127 → 130; 123 → 120.

Which rounding method should I use?

Standard half-up is the most common. Floor is used in computing (integer division). Ceiling is used in scheduling and capacity planning.

Rounding Calculator

Enter any number and choose how many decimal places to round to. Results are shown for standard rounding, floor (always down), ceiling (always up), and truncation — plus nearest 10, 100, and 1,000.

How to use this calculator

Enter the number you want to round.
Set the number of decimal places (0 = integer).
Select the rounding method and read all comparison results at once.

Formula & method

Rounding methods

Standard: round(x × 10ⁿ) / 10ⁿ · Floor: ⌊x × 10ⁿ⌋ / 10ⁿ · Ceiling: ⌈x × 10ⁿ⌉ / 10ⁿ · Truncate: trunc(x × 10ⁿ) / 10ⁿ

n = number of decimal places. Results are also shown for nearest 10, 100, and 1,000.

Example

123.4567 to 2 decimals: Standard = 123.46, Floor = 123.45, Ceiling = 123.46, Truncate = 123.45.

Key insights

Standard rounding (half-up): digits 5–9 round up, 1–4 round down. 2.5 → 3.
Floor always rounds toward −∞: floor(2.9) = 2, floor(-2.1) = -3.
Ceiling always rounds toward +∞: ceil(2.1) = 3, ceil(-2.9) = -2.
Truncation removes decimals without rounding: trunc(2.9) = 2, trunc(-2.9) = -2.

How to interpret your result

When to use floor vs ceiling

Use floor when you cannot overshoot (e.g. number of complete items). Use ceiling when you must cover all cases (e.g. number of pages needed).

Significant figures vs decimal places

Decimal places count digits after the decimal point. Significant figures count all meaningful digits from the first non-zero digit.

Frequently asked questions

What is the difference between rounding and truncation?: Rounding adjusts the last digit based on the next digit (up if ≥ 5). Truncation simply drops all digits beyond the desired precision without adjustment.
What does 'round to the nearest 10' mean?: Replace the units digit with 0, rounding up if the units digit is 5 or more. 127 → 130; 123 → 120.
Which rounding method should I use?: Standard half-up is the most common. Floor is used in computing (integer division). Ceiling is used in scheduling and capacity planning.

Related calculators

Percentage Calculator — Find X% of a number, what percent X is of Y, or the change between two values.
Long Division Calculator — Perform integer long division with remainder, mixed number result, and step-by-step verification.
Scientific Notation Calculator — Convert any number to scientific notation and perform arithmetic (add, subtract, multiply, divide) on numbers in scientific notation.

See all math calculators · Explore all online calculators