Significant Figures Calculator
Count significant figures and round numbers to a specified number of sig figs. Review how precision rules apply to each digit.
Rounding Calculator
Round numbers to any decimal place, whole number, or significant figure. Supports round half up, half down, half even, ceiling, and floor modes.
Negative values round to tens, hundreds, etc.
Result⧉
3.14
Mode: half-up
Half Up⧉
3.14
Half Even⧉
3.14
Ceiling⧉
3.15
Floor⧉
3.14
Truncate⧉
3.14
Planning notes, formulas, and examples
About the Rounding Calculator
The Rounding Calculator rounds any number to a specified number of decimal places or to the nearest whole number, ten, hundred, or thousand. Choose from multiple rounding modes including standard rounding, ceiling, floor, and banker's rounding.
Rounding is one of the most common mathematical operations. Whether you are working with currency, measurements, or data analysis, knowing how and when to round is essential for presenting clean, meaningful numbers.
This calculator handles all the edge cases: negative numbers, midpoint values (like 2.5), and very large or very small numbers. Select a rounding mode and precision, and review the rounded result.
When This Page Helps
Different rounding modes can give different results for the same input (2.5 rounds to 2 or 3 depending on the method). This calculator lets you choose the exact mode and verify the result.
How to Use the Inputs
- Enter the number you want to round.
- Choose the number of decimal places (0 for whole number, negative for tens/hundreds).
- Select a rounding mode (half up, half down, ceiling, floor, truncate).
- View the rounded result in the output panel.
- Compare different modes side by side.
Formula used
Round half up: if fractional part ≥ 0.5, round away from zero
Ceiling: ⌈x⌉ = smallest integer ≥ x
Floor: ⌊x⌋ = largest integer ≤ x
Truncate: remove decimal digits without roundingExample Calculation
Result: 3.14
Rounding 3.14159 to 2 decimal places: the third decimal is 1 (< 5), so we round down and keep 3.14.
Tips & Best Practices
- Use ceiling for billing (always round up charges).
- Use floor for conservative estimates.
- Banker's rounding (round half to even) reduces cumulative bias.
- Negative decimal places round to tens (−1), hundreds (−2), etc.
- Truncation simply removes digits without rounding.
- Financial regulations often specify which rounding mode to use.
Rounding Modes Explained
Round half up is the method taught in schools. Ceiling always rounds toward positive infinity. Floor always rounds toward negative infinity. Truncation simply cuts off digits.
When Rounding Matters
In scientific calculations, premature rounding causes cascading errors. Round only at the final step. In accounting, legal rounding rules ensure consistency across organizations.
Negative Decimal Places
Setting decimal places to −1 rounds to the nearest ten, −2 to the nearest hundred, and so on. This is useful for summarizing large data sets.
Mastering this concept provides a strong foundation for advanced coursework in mathematics, statistics, and related quantitative disciplines.
Sources & Methodology
Last updated:
Frequently Asked Questions
Round half up is the most common rule: if the digit after your place is 5 or more, round up; otherwise round down. For example, 2.5 rounds to 3.
Also called round half to even, it rounds 0.5 to the nearest even number. So 2.5 rounds to 2 and 3.5 rounds to 4. This reduces systematic bias over many calculations.
For positive numbers they are the same. For negatives, floor(−2.3) = −3 (towards −∞) while truncate(−2.3) = −2 (towards zero).
Set decimal places to −2. For example, 1,234 rounded to −2 decimal places gives 1,200.
Rounding errors accumulate across millions of transactions. Choosing the wrong method can create discrepancies of thousands of dollars. Regulations like GAAP specify rounding rules.
Yes, every rounding operation introduces a small error. Banker's rounding minimizes systematic bias because it rounds up and down equally often for midpoint values.
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