Rounding calculator

To round a number, look at the digit just after the place you are rounding to. With standard rounding (round half up), if that digit is 5 or more, round up; if it is 4 or less, round down.

Example: round 1,234.5678 to different places:

Round to	Result
Nearest thousand	1,000
Nearest hundred	1,200
Nearest ten	1,230
Nearest whole number	1,235
Nearest tenth	1,234.6
Nearest hundredth	1,234.57

The calculator shows your chosen rounding plus this whole table at once, so you can pick the precision you need. It works in your browser and avoids the tiny floating-point errors that make some tools round 1.005 the wrong way.

Most of the time you want standard rounding, but other rules have their uses:

Rule	2.5	3.5	−2.5	4.1
Half up (standard)	3	4	−3	4
Half to even (banker's)	2	4	−2	4
Always up (ceiling)	3	4	−2	5
Always down (floor)	2	3	−3	4
Truncate	2	3	−2	4

Banker's rounding sends exact halves to the nearest even digit, so rounding errors cancel out over many values. It is the default in some programming languages and accounting systems. Always up is what you want when counting things you must buy whole: 4.1 boxes of tile means buying 5.

Significant figures count meaningful digits from the first nonzero digit. They are used in science and engineering to show how precise a measurement is.

• 0.004567 to 2 significant figures = 0.0046
• 123,456 to 3 significant figures = 123,000
• 9.995 to 3 significant figures = 10.0

Leading zeros are never significant; zeros between nonzero digits always are. Trailing zeros after a decimal point (2.50) are significant because they show precision.

Dollar amounts are normally rounded to the nearest cent (hundredth). Calculate with full precision first, then round once at the end. Rounding each step can add up to noticeable errors when you add many items.

Example: 3 items at $1.333 each. Rounding each to $1.33 gives $3.99; multiplying first gives $3.999, which rounds to $4.00.

For sales tax, interest and payroll, follow the rule your state, bank or software uses, since some round each line and others round the total.

• Rounding in steps. 2.449 to the nearest whole number is 2. Rounding first to 2.45 and then to 2.5 and 3 is wrong.
• Dropping significant trailing zeros. If a measurement is 4.20 cm, writing 4.2 suggests less precision.
• Negative numbers. With half up, −2.5 rounds to −3 (away from zero), not −2.
• Rounding before comparing. Compare full values first; two different numbers can round to the same result.

To check the precision of very large or small numbers, the scientific notation calculator is also helpful.

Teachers usually ask for a specific precision, such as "round to the nearest tenth" or "give your answer to three significant figures." In science labs, the rule of thumb is that a result should not be more precise than the least precise measurement that went into it. If you measure 12.3 cm and 4.56 cm and multiply them, report the area as 56.1 cm², with three significant figures, even though the calculator shows 56.088.

In everyday estimates, rounding to friendly numbers first makes mental math easier: 498 × 21 is close to 500 × 20 = 10,000. Use the calculator afterward for the exact figure (10,458).