Rounding Calculator - Round, Ceiling, Floor, Truncate Numbers with Multiple Methods
Single Number Rounding
Enter the number you want to round
Number of decimal places (0-10)
Batch Rounding
Separate numbers with commas, semicolons, or new lines
Note: Batch rounding uses Standard Round method with the specified decimal places.
Rounding Methods Quick Reference
Basic Methods
Standard Round (Half Up)
3.14 → 3.1 (1 decimal)
3.15 → 3.2 (1 decimal)
Most common: 0.5 rounds up
Ceiling (Round Up)
3.14 → 3.2 (1 decimal)
3.01 → 3.1 (1 decimal)
Always rounds toward positive infinity
Floor (Round Down)
3.99 → 3.9 (1 decimal)
3.14 → 3.1 (1 decimal)
Always rounds toward negative infinity
Advanced Methods
Truncate (Chop)
3.99 → 3 (0 decimals)
-3.99 → -3 (0 decimals)
Removes decimals without rounding
Banker's Round
2.5 → 2 (rounds to even)
3.5 → 4 (rounds to even)
Reduces cumulative error in finance
Significant Figures
1234 → 1230 (3 sig figs)
0.001234 → 0.00123 (3 sig figs)
Used in science and engineering
Understanding Different Rounding Methods
1. Standard Rounding (Half Up)
The most common method. If the digit after the rounding position is 5 or greater, round up; otherwise, round down.
Examples:
3.14 → 3.1 (1 decimal place)
3.15 → 3.2 (1 decimal place)
2.449 → 2.45 (2 decimal places)
7.5 → 8 (0 decimal places)
2. Ceiling (Round Up)
Always rounds toward positive infinity. The result is never less than the original number.
Examples:
3.14 → 3.2 (1 decimal place)
3.01 → 3.1 (1 decimal place)
7.001 → 8 (0 decimal places)
Use case: Calculate minimum packages needed
3. Floor (Round Down)
Always rounds toward negative infinity. The result is never greater than the original number.
Examples:
3.99 → 3.9 (1 decimal place)
3.14 → 3.1 (1 decimal place)
7.999 → 7 (0 decimal places)
Use case: Calculate complete units produced
4. Truncate (Chop)
Simply removes digits after the specified position without any rounding logic.
Examples:
3.999 → 3.99 (2 decimal places)
3.14159 → 3.14 (2 decimal places)
7.999 → 7 (0 decimal places)
Use case: Remove fractional cents in billing
5. Banker's Rounding (Round Half to Even)
When the digit is exactly 5, rounds to the nearest even number. Reduces cumulative bias in large datasets.
Examples:
2.5 → 2 (rounds to even)
3.5 → 4 (rounds to even)
4.5 → 4 (rounds to even)
Use case: Financial calculations, statistical analysis
6. Significant Figures
Rounds to a specified number of significant (meaningful) digits, regardless of decimal position.
Examples (3 sig figs):
1234 → 1230
0.001234 → 0.00123
123.456 → 123
Use case: Scientific measurements, engineering
When to Use Each Rounding Method
💰 Finance & Business
- • Banker's Rounding: Large transaction volumes
- • Standard Round: Currency display ($19.99 → $20)
- • Truncate: Remove fractional cents
- • Ceiling: Minimum order quantities
🔬 Science & Engineering
- • Significant Figures: Measurement precision
- • Standard Round: General calculations
- • Truncate: Digital signal processing
- • Floor/Ceiling: Discrete quantities
📊 Statistics & Data
- • Banker's Rounding: Reduce cumulative error
- • Standard Round: Data presentation
- • Significant Figures: Survey data
- • Floor: Histogram bins
💻 Programming
- • Truncate: Integer conversion
- • Floor/Ceiling: Array indexing
- • Standard Round: Display values
- • Banker's Rounding: Financial APIs
Common Rounding Mistakes to Avoid
❌ Mistake #1: Rounding Multiple Times
Wrong: 3.14159 → 3.142 → 3.14
Right: 3.14159 → 3.14 directly
Multiple rounds accumulate errors. Always round once from the original number.
❌ Mistake #2: Using Wrong Method
Wrong: Using standard rounding for large financial datasets
Right: Use banker's rounding to prevent bias
Standard rounding creates upward bias when processing millions of values.
❌ Mistake #3: Too Many Significant Figures
Wrong: Measuring with a ruler (±1mm) → 15.73482 cm
Right: Measuring with a ruler → 15.7 cm
Don't imply false precision. Use sig figs that match your measurement tool.
❌ Mistake #4: Confusing Floor and Truncate
For negative numbers, they differ:
Floor: -3.7 → -4 (toward negative infinity)
Truncate: -3.7 → -3 (toward zero)
Know which one your application needs!
Tips for Batch Rounding
Our calculator supports batch rounding of multiple numbers at once. Here are some tips:
- Separate numbers with commas, semicolons, or new lines
- Mix of positive and negative numbers is supported
- Invalid numbers are automatically skipped
- Use "Copy All Results" to get all rounded values at once
- Great for processing data from spreadsheets or lists
Example Input:
3.14159 2.71828 1.41421 0.57721