Rounding Calculator
All Rounding Results
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How Rounding Works
Rounding is the process of reducing the number of digits in a number while keeping its value close to the original. It is one of the most fundamental operations in mathematics, used constantly in science, engineering, finance, and everyday life. When you check the weather and see "72 degrees" instead of "72.384 degrees," rounding has already done its work. This calculator lets you compare six different rounding methods side by side, so you can choose the right one for your situation.
Rounding to Decimal Places
Rounding to decimal places controls how many digits appear after the decimal point. To round 3.14159 to 2 decimal places, you look at the third decimal digit (1). Since 1 is less than 5, you round down to get 3.14. If the number were 3.14659, the third digit (6) is 5 or greater, so you round up to 3.15. This method is the most commonly used form of rounding and appears in currency calculations (2 decimal places), scientific measurements, and grade calculations.
Rounding to Significant Figures
Significant figures count all meaningful digits starting from the first non-zero digit. The number 0.004562 has four significant figures (4, 5, 6, 2), while 12,300 might have 3, 4, or 5 depending on context. Rounding to significant figures is standard practice in scientific measurements because it reflects the precision of the measuring instrument. If your scale measures to the nearest gram, reporting a mass as 45.2 g (3 sig figs) is appropriate, while 45.2381 g would imply false precision.
Rounding Methods Explained
Round Half Up (Standard): The most common method. When the digit after the rounding position is exactly 5, round away from zero. Example: 2.5 becomes 3, and -2.5 becomes -3. This is the method taught in most schools.
Round Half Down: When the digit is exactly 5, round toward zero. Example: 2.5 becomes 2, and -2.5 becomes -2. This method is less common but used in some financial contexts.
Round Half Even (Banker's Rounding): When the digit is exactly 5, round to the nearest even number. Example: 2.5 becomes 2, but 3.5 becomes 4. This eliminates systematic upward bias in large datasets and is the default in IEEE 754 floating-point arithmetic, Python's built-in round() function, and many banking systems. It is called "banker's rounding" because financial institutions use it to prevent cumulative rounding errors across millions of transactions.
Floor: Always rounds toward negative infinity. Example: 2.7 becomes 2, and -2.3 becomes -3. Use this when you need to know how many complete units fit into something, such as how many full boxes you can fill.
Ceiling: Always rounds toward positive infinity. Example: 2.1 becomes 3, and -2.7 becomes -2. Use this when you need to ensure you have enough, such as how many buses are needed to transport a group of people.
Truncate: Simply removes digits beyond the rounding position without any rounding logic. Example: 2.9 becomes 2, and -2.9 becomes -2. This rounds toward zero and is equivalent to the integer conversion in many programming languages.