Number Rounding Calculator

Number rounding is the process of replacing a number with an approximation that has fewer significant digits or a simpler representation. Rounding is used to reduce precision to a meaningful level, simplify calculations, and present results in a readable format. Our number rounding calculator supports 10 rounding modes — decimal places, significant figures, nearest integer, nearest 0.5, nearest 0.25, nearest 0.1, nearest power of 10, floor, ceiling, and truncate — with 4 tie-breaking rules for handling the exact midpoint case (e.g. 2.5).

1. Enter Your Number: Type any number into the number rounding calculator — integers, decimals, negative numbers, and very small or large values are all supported. Click any preset button to load a common example instantly.
2. Select Rounding Mode and Parameters:Choose from 10 rounding modes. For decimal places and significant figures, enter the target precision. For nearest power of 10, enter the exponent (e.g. 2 = nearest 100). For modes that involve tie-breaking (e.g. 2.5), choose your preferred rule: half-up, half-down, half-even (banker's), or half-away-from-zero.
3. View Results: The number rounding calculator displays the rounded result, the rounding error (original − rounded), step-by-step scaling formulas, and a comparison table showing all 7 rounding methods applied to your number simultaneously — all processed locally in your browser.

• Decimal Places: Round to n digits after the decimal point. 3.14159 rounded to 2 dp = 3.14. Uses the scaling formula: multiply by 10ⁿ, round to integer, divide by 10ⁿ.
• Significant Figures: Round to n total significant digits, regardless of magnitude. 1234.5 to 3 sig figs = 1230; 0.00456 to 2 sig figs = 0.0046. Preserves the relative precision of the number.
• Nearest Power of 10: Round to the nearest 10, 100, 1000, etc. (or 0.1, 0.01 for negative powers). 1234 rounded to nearest 100 (10²) = 1200.
• Floor, Ceiling, Truncate: Floor always rounds toward −∞ (⌊3.7⌋ = 3, ⌊−3.7⌋ = −4). Ceiling always rounds toward +∞ (⌈3.2⌉ = 4). Truncate always rounds toward 0 (trunc(3.7) = 3, trunc(−3.7) = −3).

When a number is exactly halfway between two rounded values (e.g. 2.5 between 2 and 3), different rounding rules give different results. Half-up (the most common) always rounds 0.5 toward +∞ (2.5 → 3, −2.5 → −2). Half-away-from-zero rounds 0.5 away from zero (2.5 → 3, −2.5 → −3). Half-even (banker's rounding) rounds 0.5 to the nearest even number (2.5 → 2, 3.5 → 4) — this minimizes cumulative rounding bias and is the default in Python 3, IEEE 754, and many financial systems. Half-down always rounds 0.5 toward −∞ (2.5 → 2, −2.5 → −3).