Rounding Calculator

Round a number to decimal places, significant figures or the nearest 10, 100 or any multiple, using the rounding rule you need — with the neighbors, the halfway point and the rule written out.

Typed digits are used exactly, so 2.665 really is 2.665.

2.665 rounded
2.67
Half up
Rounded to the nearest
0.01
Neighbors
2.66 and 2.67
Rounding error (rounded − original)
+0.005
  • Rounding to 2 decimal places means rounding to the nearest 0.01 (the hundredths place).
  • Mark the cut after the hundredths digit: 2.66 | 5. Everything after the bar is being dropped.
  • 2.665 lies between 2.66 and 2.67. It is 0.005 above 2.66 and 0.005 below 2.67, so it is exactly halfway between them.
  • Half up rounds an exact half away from zero, so the answer is 2.67.

2.665 under every rounding rule

RuleResult
Half up2.67
Half to even2.66
Half down2.66
Up (away from zero)2.67
Down (truncate)2.66
Ceiling2.67
Floor2.66

How rounding works

Every rounding question is really "which multiple of the step size is closest?" Rounding to 2 decimal places means rounding to the nearest 0.01; rounding to the nearest hundred means the nearest multiple of 100; rounding to 3 significant figures means rounding at the third digit counted from the first nonzero one. Find the two neighbors on either side of your number, see which is closer, and use a rule to break ties.

The school method: look at the first digit you're dropping. If it's 5 or more, round up; if it's 4 or less, leave the kept digits alone. That works for every case except an exact half, where the rounding rule decides.

Rounding rules compared

Half up (half away from zero) is what most people learn in school: 2.5 becomes 3 and -2.5 becomes -3. Half to even, also called banker's rounding, sends an exact half to the even neighbor: 2.5 becomes 2, 3.5 becomes 4. Because ties go up half the time and down half the time, it avoids the upward drift that half up causes when you round and add many numbers. NIST's guide to the SI and OpenStax's chemistry textbook both describe this round-half-to-even rule for dropping a final 5.

Up (away from zero) and down (toward zero, or truncation) ignore which neighbor is closer. Truncation is what happens when you simply chop off digits. Ceiling and floor go toward positive and negative infinity: they match up and down for positive numbers but differ for negatives, since the ceiling of -2.1 is -2 while rounding -2.1 up (away from zero) gives -3.

Decimal places vs. significant figures

Decimal places count digits after the decimal point, so they suit money (2 places for cents) and fixed units. Significant figures count from the first nonzero digit, so they keep the same relative precision for big and small numbers: 0.0045678 and 45,678 both round to three significant figures as 0.00457 and 45,700.

Keep trailing zeros that rounding produces. 2.996 rounded to 2 decimal places is 3.00, not 3 — the zeros say the value is known to the hundredth.

Why some software rounds 2.675 to 2.67

Computers usually store numbers in binary, and most decimals can't be stored exactly. The value saved for 2.675 is a hair below 2.675, so JavaScript's (2.675).toFixed(2) returns 2.67 even though the school rule gives 2.68. This calculator works on the digits you type, so 2.675 is treated as exactly 2.675.

Rounding to a step size

Lower neighbor L = the largest multiple of s that is ≤ x; upper neighbor U = L + sRound to L if x − L < s ÷ 2; to U if x − L > s ÷ 2; if x − L = s ÷ 2, the rounding rule decidesDecimal places d: s = 10⁻ᵈ. Significant figures k: s = 10^(p − k + 1)
  • x = the number being rounded
  • s = the step: 0.01, 100, 0.25 and so on
  • p = the place value (power of ten) of the first nonzero digit of x

Worked examples

  1. 2.665 to 2 decimal places: the neighbors are 2.66 and 2.67, and 2.665 is exactly halfway. Half up gives 2.67; half to even gives 2.66, because 6 is even.
  2. -2.5 to a whole number: half up gives -3, half to even gives -2, ceiling gives -2 and floor gives -3.
  3. 1,234.5 to the nearest 100: the neighbors are 1,200 and 1,300, and 1,234.5 is 34.5 above 1,200, nearer than 1,300. The answer is 1,200.
  4. 0.0045678 to 3 significant figures: the first significant digit is in the thousandths place, so round to the nearest 0.00001. The answer is 0.00457.

Frequently asked questions

Does 5 round up or down?

With the usual school rule (half up), a 5 followed by nothing else rounds up: 2.5 becomes 3. With half to even (banker's rounding), it goes to the even neighbor: 2.5 becomes 2 and 3.5 becomes 4. If anything nonzero follows the 5, as in 2.51, every half rule rounds up.

What is banker's rounding?

Another name for round half to even. Exact halves go to the nearest even digit, so ties round up and down equally often and totals don't drift upward. It's the rule described in NIST's guide to the SI.

How do I round to the nearest 0.5 or quarter?

Choose "nearest multiple" and enter 0.5 or 0.25. For example, 7.3 rounded to the nearest 0.25 is 7.25, because 7.3 is 0.05 above 7.25 and 0.2 below 7.5.

How do I round a negative number?

Round its size the same way and keep the minus sign for the half-up, half-even, up and down rules: -2.7 becomes -3. Ceiling and floor are different: the floor of -2.1 is -3 and the ceiling is -2.

Should I round in the middle of a calculation?

No. Keep full precision until the end and round only the final answer. Rounding early lets small errors add up.

Sources

Last reviewed for 2026. How we calculate.