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Floor Function Calculator.

Calculate floor(x), the greatest integer less than or equal to x.

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Floor: 3

Floor

0.000000

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Use Cases

Rounding down in programming and math

Use the floor function to implement integer division, array indexing, or discretize continuous values. It's essential in algorithms that require the largest integer not exceeding a given number.

Example: In Python, math.floor(7.8) returns 7, which is useful for pagination or time calculations.

Solving equations and inequalities

When working with floor equations or inequalities, quickly compute floor values to check solutions or simplify expressions. This calculator provides instant results for verification.

Example: Solve floor(x) = 5: any x in [5,6) works; the calculator confirms floor(5.999) = 5.

Frequently Asked Questions

What does the floor function do?
The floor function maps a real number x to the greatest integer that is less than or equal to x. For example, floor(3.7) = 3 and floor(-2.3) = -3. It effectively rounds down to the nearest integer, even for negative numbers.
How is floor different from rounding down?
Rounding down (or truncation) removes the decimal part, moving toward zero. The floor function always moves toward negative infinity. For positive numbers they are the same, but for negatives they differ: floor(-2.3) = -3, while truncation gives -2.
Can I use this calculator for negative numbers?
Yes, the calculator accepts any real number for x, including negatives. It correctly applies the floor definition, so for negative inputs the result is the next lower integer (e.g., floor(-0.5) = -1).

Tips & Common Mistakes

Tips

  • For positive numbers, floor(x) is simply the integer part. For negative numbers, subtract 1 from the integer part if there is a fractional part.
  • Remember that floor(x) ≤ x < floor(x)+1. This property is useful for bounding values in calculations.
  • If you need to round to the nearest integer, use round(x) instead; floor always rounds down.
  • When using this calculator, enter the exact value of x, including decimals or fractions, to get the correct floor.

Common Mistakes to Avoid

  • Confusing floor with truncation: floor(-2.3) is -3, not -2. Always consider the direction toward negative infinity.
  • Assuming floor(x) equals the integer part for all numbers: it fails for negative numbers with a fractional part.
  • Forgetting that floor(x) is the greatest integer less than or equal to x, so for integer x, floor(x) = x itself.

Last updated: August 13, 2026