⬇️ Floor Function Calculator
Round down to nearest integer
How to Use This Calculator
Enter Any Number
Type any decimal or integer in the input field. Examples: 3.7, -2.3, 5, 0.1
Click Calculate Floor
Press the "Calculate Floor" button to round down and see ceiling, rounded, and truncated values.
Compare Results
See floor (rounds down), ceiling (rounds up), rounded (nearest), and truncated (remove decimals) values.
Formula
⌊x⌋ = greatest integer ≤ x
Floor rounds DOWN to previous integer
Example 1: ⌊3.1⌋
Greatest integer ≤ 3.1 is 3
Floor = 3
Example 2: ⌊3.9⌋
Greatest integer ≤ 3.9 is 3
Floor = 3
Example 3: ⌊-3.7⌋
Greatest integer ≤ -3.7 is -4
Floor = -4
Example 4: ⌊5⌋
Greatest integer ≤ 5 is 5
Floor = 5 (already integer)
About Floor Function Calculator
The Floor Function Calculator rounds numbers down to the nearest integer. The floor function, denoted ⌊x⌋, returns the greatest integer that is less than or equal to x. This is useful for truncating values, age calculations, and integer division results.
When to Use This Calculator
- Truncation: Remove decimal parts (always round down)
- Age Calculations: Calculate age from birthdate
- Bucketing: Group values into integer ranges
- Mathematics: Solve floor function problems
- Programming: Understand Math.floor() behavior
- Business: Calculate maximum quantities or capacities
Why Use Our Calculator?
- ✅ Visual Comparison: See floor, ceiling, rounded, and truncated together
- ✅ Instant Results: Calculate all rounding methods instantly
- ✅ Educational: Learn difference between rounding functions
- ✅ Practical Examples: Understand when to use each method
- ✅ Negative Support: Works with negative numbers correctly
- ✅ Completely Free: No registration required
Floor vs Ceiling vs Round vs Truncate
All rounding functions behave differently:
- Floor ⌊x⌋: Always rounds DOWN (3.9 → 3, -3.1 → -4)
- Ceiling ⌈x⌉: Always rounds UP (3.1 → 4, -3.9 → -3)
- Round: Rounds to NEAREST integer (3.5 → 4, 2.4 → 2)
- Truncate: Removes decimals (3.7 → 3, -3.7 → -3)
Real-World Applications
Truncating Prices: If an item costs $19.99, floor gives you ⌊19.99⌋ = $19 for cash calculations.
Age Calculations: A person born in 1995 is ⌊2024 - 1995⌋ = ⌊29⌋ = 29 years old in 2024.
Capacity: If you have 15.7 people per room, you need ⌊15.7⌋ = 15 rooms minimum.
Tips for Using This Calculator
- Floor always rounds DOWN, even for large decimals like 3.9
- Negative numbers: ⌊-3.7⌋ = -4 (more negative is lower)
- Integers stay the same: ⌊5⌋ = 5
- Use floor when you need to guarantee rounding down
- Compare with ceiling to see the difference
- In programming, Math.floor() is the floor function
Frequently Asked Questions
What's the difference between floor and ceiling?
Floor rounds DOWN (3.9 → 3), ceiling rounds UP (3.1 → 4). For 3.5: floor = 3, ceiling = 4.
How does floor work with negative numbers?
Floor still rounds DOWN (more negative). ⌊-3.7⌋ = -4, ⌊-3.1⌋ = -4, ⌊-3⌋ = -3.
Is floor the same as truncate?
For positive numbers, yes! But for negatives: ⌊-3.7⌋ = -4, while truncate(-3.7) = -3. Floor always rounds down.
What's floor of an integer?
The floor of an integer is itself. ⌊5⌋ = 5, ⌊-3⌋ = -3. No rounding needed.
When should I use floor instead of round?
Use floor when you must round DOWN (age, capacity, minimum requirements). Use round for nearest approximation.
What's the floor symbol?
The floor function uses ⌊x⌋ notation (downward-pointing brackets). In code: Math.floor() or floor(x).