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Ceiling and floor function calculator

The ceiling ⌈x⌉ rounds up to the next integer, the floor ⌊x⌋ rounds down. Enter any number to get both, plus the ordinary round, the truncation toward zero and the fractional part left over.

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Enter Number and the Ceiling and floor function calculator works out Ceiling ⌈x⌉, Floor ⌊x⌋, Rounded, Truncated, Fractional part straight away. For instance, with Number = 3.7 it returns Ceiling ⌈x⌉ = 4, Floor ⌊x⌋ = 3 and Rounded = 4.

How to use it

  1. Enter your values: Number.
  2. Read the result instantly: Ceiling ⌈x⌉, Floor ⌊x⌋, Rounded, Truncated, Fractional part.

Frequently asked questions

What does the Ceiling and floor function calculator actually compute?

It takes Number and derives Ceiling ⌈x⌉, Floor ⌊x⌋, Rounded, Truncated and Fractional part from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

A single value: Number. Nothing else is required — no account, no file upload.

Can you show a worked example?

With Number = 3.7, the calculator returns Ceiling ⌈x⌉ = 4, Floor ⌊x⌋ = 3 and Rounded = 4. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Number = 7.4 instead, Ceiling ⌈x⌉ goes from 4 to 8 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Number = 1.85, Ceiling ⌈x⌉ comes out at 2. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Reading a number written another way: a Roman numeral on a monument, a hexadecimal colour, a binary byte, or a fraction that needs reducing.

What is the most common mistake?

Assuming a decimal fraction survives a change of base. A tenth is exact in decimal and infinitely repeating in binary, which is why 0.1 + 0.2 is not 0.3 in most programming languages.

What is the difference between the Ceiling and floor function calculator and the Partition function calculator?

This one returns Ceiling ⌈x⌉ and Floor ⌊x⌋; the Partition function calculator returns p(n) — number of partitions and Number of digits. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Beta Function Calculator is the closest one after this: Compute the Euler Beta function B(x, y) = Γ(x)·Γ(y) / Γ(x+y) via a stable log-gamma.

What else is worth having open alongside it?

Complementary Error Function Calculator and Error Function Calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
How-toHow to Round Numbers: Round Half Up, Round Half to Even, and MoreRound to any decimal place or number of significant figures, and learn when to use round half up versus round half to even to avoid bias.ExplainerSignificant Figures Explained: Counting, Rounding, and Why They MatterLearn what counts as a significant figure, the rules for leading, trailing, and captive zeros, and how sig figs keep your calculated answers honest.How-toHow to Find Prime Factors: Factor Trees and the Division MethodBreak any whole number into its prime building blocks with a factor tree or repeated division — and write the result as a clean prime factorization with exponents.How-toHow to Multiply and Divide Fractions: Multiply Across, Flip to DivideMultiplying fractions needs no common denominator — just multiply across. Dividing means multiplying by the reciprocal. Learn both with worked examples and how to simplify.How-toHow to Add and Subtract Fractions: Common Denominator, Combine, SimplifyYou can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.How-toHow to Do Long Division: Divide, Multiply, Subtract, Bring DownLong division breaks a big division into a repeating four-step cycle. Learn the divide-multiply-subtract-bring-down loop and how to read the remainder, with a worked example.