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Rounding Calculator

By Calxy · Updated · Calculation methodology

Round a number to decimal places, tens or a chosen multiple. Pick a rounding method, see the kept digit and the discarded part, and compare all eight methods.

Printed from Calxy · https://www.calxy.net/math/rounding-calculator

Rounded number1234.57

places

How many digits to keep after the decimal point. Use 0 for a whole number, −1 for tens, −2 for hundreds.

Rounded number

1234.57

  • MethodHalf away from zero
  • Discarded part (in kept-place units)0.78
Every method applied to 1234.5678
MethodRuleResult
Half away from zero (selected)Ties move away from zero: 2.5 → 3, −2.5 → −31234.57
Half up (toward +∞)Ties move toward positive infinity: 2.5 → 3, −2.5 → −21234.57
Half down (toward −∞)Ties move toward negative infinity: 2.5 → 2, −2.5 → −31234.57
Half to even (banker’s)Ties go to the even neighbour: 2.5 → 2, 3.5 → 41234.57
Half toward zeroTies move toward zero: 2.5 → 2, −2.5 → −21234.57
Ceiling (always up)Any discarded part moves toward +∞: 2.1 → 3, −2.9 → −21234.57
Floor (always down)Any discarded part moves toward −∞: 2.9 → 2, −2.1 → −31234.56
Truncate (toward zero)Drop the discarded part: 2.9 → 2, −2.9 → −21234.56

Uses decimal half-away-from-zero rounding, so 2.5 → 3 and −2.5 → −3 at zero decimal places. Different accounting or programming systems may use half-to-even instead; the table compares every method.

How this was calculated

  1. Find the last digit you keep: it sits in the hundredths place. Everything after it is the part you drop.Keep 2 decimal places: the last kept digit is in the hundredthsPut in your numbers: 1234.5678 → kept part 1234.56, retained digit 6Answer: Discarded part = 0.78 of one unit in the hundredths
  2. The part you drop is more than half of one step in that place. With your rounding method, that means you add 1 to the last kept digit (moving away from zero).Decide (half away from zero)Put in your numbers: Discarded part 0.78 > 0.5; the number is nonnegative, so add 1 to the last kept digit (moving away from zero)Answer: 1234.57Ties move away from zero: 2.5 → 3, −2.5 → −3

Rounding in simple words

Rounding makes a number shorter and easier to use, while keeping it close to the real value.

First pick the last digit you want to keep. Then look at the digit just after it. If that digit is 5 or more, add 1 to the kept digit. If it is 4 or less, leave the kept digit alone. Drop everything after it.

For example, to round 1234.5678 to 2 decimal places, keep 1234.56 and look at the next digit, 7. Seven is 5 or more, so round up to 1234.57.

Rounding to the nearest 10 works the same way: 47 becomes 50, because 7 is 5 or more. This calculator can also round to other multiples, such as the nearest 5 or 0.25.

Formula and method

When the discarded part is at least half of a unit in the retained place, increase the magnitude by one unit. Negative places round left of the decimal.

Worked example

1.005 rounds to 1.01 at two decimal places. At zero places, −2.5 rounds to −3. At −2 places, 1,250 rounds to 1,300.

Rounding methods compared

The half methods differ only on an exact tie, where the discarded part is exactly half a unit. Half away from zero sends 2.5 to 3 and −2.5 to −3. Half up sends ties toward positive infinity (−2.5 → −2), half down toward negative infinity (2.5 → 2), and half to even picks the even neighbour (2.5 → 2, 3.5 → 4).

The directed methods ignore how large the discarded part is. Ceiling always moves toward positive infinity, floor toward negative infinity, and truncation simply drops the discarded digits, which moves toward zero.

NIST SP 811 (§B.7.1) gives the half-to-even rule for an exact tie: 6.974 950 5 rounded to 7 digits is 6.974 950, and 6.974 951 5 is 6.974 952. Choosing half to even here reproduces those examples.

Rounding to a multiple

To round x to the nearest multiple of m, divide, round the quotient to a whole number, then multiply back: result = round(x ÷ m) × m. The division is exact, so decimal multiples such as 0.25 or 0.05 do not pick up floating-point error.

Example: 52 minutes to the nearest 15 is 52 ÷ 15 = 3.466…, which rounds to 3, and 3 × 15 = 45. With ceiling, it becomes 4 × 15 = 60. Rounding 1.13 to the nearest 0.25 gives 4.52 → 5 → 1.25.

Frequently asked questions

Is this the same as banker’s rounding?

Not by default. The default is half away from zero, so 2.5 → 3. Choose “Half to even (banker’s)” to send exact ties to the even digit instead: 2.5 → 2 and 3.5 → 4. The comparison table shows both.

What is the difference between rounding down and truncating?

For positive numbers they agree. For negative numbers, floor (round down) moves toward negative infinity, so −2.1 → −3, while truncation drops the decimals and moves toward zero, so −2.1 → −2.

How do I round to the nearest 5 or quarter?

Choose “The nearest multiple” and enter 5, 0.25 or any positive step. The steps show x ÷ m, the rounded quotient and the final multiple.

References

Last updated . Results are estimates for informational purposes only.