How rounding, ceiling, and floor are calculated
Each value is computed at the decimal place you choose. Rounding applies round-half-up; ceiling always moves toward the larger value; floor always moves toward the smaller value.
- decimal places — how many digits after the decimal point to round to
- rounded — round-half-up result
- ceiling — value rounded up to the chosen place
- floor — value rounded down to the chosen place (toward the smaller value, not toward zero)
More detail
What round-half-up means
If the digit right after the chosen decimal place is 5 or greater, the last kept digit rounds up; otherwise it stays the same. At 0 decimal places a negative half also rounds toward positive infinity — so −2.5 rounds to −2, not −3 (Excel's ROUND function gives −3 instead). From 1 decimal place up that direction is not guaranteed, because a decimal half has no exact binary form: −0.035 at 2 places gives −0.04, not the −0.03 the rule would predict. For example, rounding 3.14159 to 2 decimal places looks at the third-place digit (1), which is below 5, so the result is 3.14.
Ceiling and floor with negative numbers
Ceiling always moves toward the larger value and floor always moves toward the smaller value — with negative numbers that can feel reversed from "rounding toward zero." For example, rounding −2.567 to 1 decimal place gives a ceiling of −2.5 and a floor of −2.6, so the floor result is actually farther from zero.
Practical tip. Use ceiling when a value must never come up short (e.g. tax or pricing rules that always round up), floor when trailing decimals can simply be dropped (e.g. some aggregate counts), and standard rounding for most on-screen display.
Frequently asked questions
What is 3.14159 rounded to 2 decimal places?
Entering 3.14159 with 2 decimal places above gives a rounded value of 3.14, a ceiling of 3.15, and a floor of 3.14 — because the digit after the second decimal place (1) is below 5, standard rounding keeps it at 3.14.
What's the difference between rounding up (ceiling) and standard rounding?
Ceiling always moves to the next larger value at the chosen decimal place, even if the dropped digits are tiny — e.g. 2.501 rounded up to 1 decimal place gives 2.6. Standard rounding only goes up when the next digit is 5 or more, so 2.501 there still rounds to 2.5.
How does ceiling/floor work with negative numbers?
Ceiling moves toward the larger (less negative) value and floor moves toward the smaller (more negative) one. For −2.567 at 1 decimal place, the ceiling above is −2.5 and the floor above is −2.6 — the floor result is actually farther from zero, opposite of what "round down" might suggest.
What happens if I set decimal places to 0?
0 decimal places rounds to a whole number. For example 2.5 with 0 decimal places gives a rounded value of 3, a ceiling of 3, and a floor of 2 — enter your own number above to see it applied.