Rounding Calculator
Round numbers to any decimal place or significant figure. Supports 6 rounding modes: half-up, half-down, half-even, ceiling, floor, and truncation.
Enter a number and click Calculate.
How Does the Formula Work?
The rounding calculator rounds numbers to any precision using six different rounding modes. It supports rounding to decimal places (including negative places for tens, hundreds, or thousands) and significant figures. The all-modes comparison table shows how each method handles the same input, which is essential when different contexts require different rounding behaviors.
Half Up (Standard): 2.5 → 3, -2.5 → -3 (away from zero)
Half Down: 2.5 → 2, -2.5 → -2 (toward zero on .5)
Half Even (Banker's): 2.5 → 2, 3.5 → 4 (to nearest even)
Ceiling: 2.1 → 3, -2.9 → -2 (toward +∞)
Floor: 2.9 → 2, -2.1 → -3 (toward −∞)
Truncate: 2.9 → 2, -2.9 → -2 (toward zero)
Decimal Places: round at the Nth digit after the decimal
Significant Figures: round at the Nth meaningful digit
Negative places: -1 = tens, -2 = hundreds
Example: 1234 to -1 decimal places = 1230
When to Use Each Mode
Half Up is the standard rounding taught in schools and used in most everyday situations. Half Even (Banker's) is required in financial calculations, IEEE 754 floating-point arithmetic, and statistical work because it eliminates the systematic upward bias that half-up rounding introduces when processing large datasets. Ceiling is used when you need to round up to ensure sufficiency — for example, calculating how many items to order. Floor rounds down, useful for calculating the maximum number of complete units that fit. Truncate simply removes digits, commonly used in programming and time calculations (e.g., 2.7 hours = 2 complete hours).
Decimal Places vs Significant Figures
Decimal places count digits after the decimal point. Significant figures count meaningful digits from the first non-zero digit. The choice depends on context: decimal places are used in currency (always 2 for dollars/euros), measurement precision, and everyday math. Significant figures are used in scientific measurements where the number of meaningful digits reflects the precision of the measuring instrument — measuring 0.00123 meters with 3 significant figures means the measurement is precise to the nearest 0.00001 meter.
Negative Decimal Places
Setting decimal places to negative values rounds to the left of the decimal point. Using -1 rounds to the nearest ten, -2 to the nearest hundred, and -3 to the nearest thousand. This is useful in statistics (rounding population figures), business (revenue to nearest million), and data presentation where excessive precision is misleading.
Rounding Error
The calculator shows the rounding error — the difference between the original value and the rounded result. This matters in scientific computing, financial calculations, and engineering where accumulated rounding errors can compound. Banker's rounding (half-even) minimizes cumulative error in large datasets because the rounding direction on .5 values is statistically balanced.
Tips & Recommendations
Half-up, half-down, banker's, ceiling, floor, and truncate. See how all 6 handle the same number in the comparison table.
Use -1 for tens, -2 for hundreds, -3 for thousands. Round 1234 to the nearest hundred = 1200.
Switch to sig figs for scientific notation. Counts from the first non-zero digit — useful for lab work and engineering.
Every calculation shows all 6 modes side by side. Compare results to pick the right rounding for your context.
Frequently Asked Questions
What rounding modes are available?
Six modes: Half Up (standard — 2.5 rounds to 3), Half Down (2.5 rounds to 2), Half Even/Banker's (2.5 rounds to 2, 3.5 rounds to 4), Ceiling (always up), Floor (always down), and Truncate (cut off decimals).
What is banker's rounding?
Also called half-even rounding. When the value is exactly 0.5, it rounds to the nearest even number. This eliminates statistical bias in financial calculations because .5 values go up half the time and down half the time.
What are significant figures?
Significant figures count meaningful digits from the first non-zero digit. For example, 0.00123 has 3 significant figures, and 9876 rounded to 2 significant figures is 9900.
Can I round to tens or hundreds?
Yes. Use negative decimal places: -1 rounds to tens (1234 → 1230), -2 rounds to hundreds (1234 → 1200), -3 rounds to thousands.
What is the difference between floor and truncate?
For positive numbers they are identical. For negative numbers: floor(-2.5) = -3 (toward negative infinity) while truncate(-2.5) = -2 (toward zero).
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