Floor & Ceiling Calculator – Round Any Number

Floor and ceiling bracket a number between the integers just below and just above it. For 2.7: floor drops to 2 and ceiling rises to 3. Negatives flip intuition — floor(−2.1) = −3 (not −2!) because −3 is the greatest integer still ≤ −2.1, while ceil(−2.1) = −2. The calculator prints both functions side by side with the integer interval they form, and contrasts truncation, which merely deletes decimals and agrees with floor only for positives (trunc(−2.1) = −2 ≠ floor). Real logic leans on these functions daily: ceiling determines how many 6-person tables seat 20 guests (⌈20/6⌉ = 4), floor converts 250 seconds to whole minutes (⌊250/60⌋ = 4), and pagination computes page = ⌊index/itemsPerPage⌋. Exact integers pass through unchanged: floor(5) = ceil(5) = 5.

1. 1

   Enter any real number

   Positive, negative, decimal — both functions are computed

2. 2

   Read the floor

   The greatest integer less than or equal to your input

3. 3

   Read the ceiling

   The smallest integer greater than or equal to your input

4. 4

   Compare with truncation

   Differences appear for negative inputs

• 1

  floor(−2.1) = −3 — negatives round away from zero on floor

• 2

  ceil(b/a) answers "how many groups of a cover b"

• 3

  Integers are fixed points: floor(5) = ceil(5) = 5

• Assuming floor(−2.1) = −2; it is −3

• Mixing up which of the two rounds toward zero for negatives

• Using ceiling when whole groups are wasted — 20/6 needs 4 tables (ceil), not 3

• Confusing truncation with floor for negative decimals