Round a number to the decimal place, power of ten or fraction you need, and compare what each rounding rule gives.
Most numbers round the same way under every rule: 2.4 goes down to 2 and 2.6 goes up to 3. The rules only disagree on the exact halfway case, like 2.5, where the number is just as close to 2 as it is to 3. Each mode is a different answer to the question “what do we do with a tie?”. The table under the result shows your number under all nine modes at once, so you can see exactly where they differ and pick the one your task requires.
Take 2.5 and round to the nearest whole number. Half up and half away from zero give 3. Half down gives 2. Half to even gives 2, because 2 is the even neighbour. Half to odd gives 3. Now try 3.5: half to even gives 4, because 4 is even. This is why half to even is sometimes called “banker’s rounding”: over many ties it rounds down about as often as it rounds up. The calculator works with exact decimal digits, so 1.45 rounded to one decimal place is a true tie and is handled like one, with none of the floating-point surprises you get in many programming languages.
For school maths and everyday use, the default (round to the nearest, with ties going away from zero) is what teachers expect. For accounting, statistics and scientific data, half to even is often preferred because it avoids a built-in upward bias. Rounding the four numbers 0.5, 1.5, 2.5 and 3.5, which really add up to 8, gives 10 with half up but exactly 8 with half to even. Ceiling and floor are not about ties at all: ceiling always moves toward larger numbers and floor toward smaller ones, which is what you want when you must never underestimate, such as the number of boxes needed to hold 17.2 litres.
With negatives, “up” and “away from zero” are different things. Round −2.5 half up and you get −2, because up means toward the larger number. Round it half away from zero and you get −3. Floor of −2.6 is −3, while simply chopping off the decimals (rounding toward zero) would give −2. If your negative results look wrong by one, check the mode first.
Choose tens, hundreds, thousands or millions to round large numbers, so 1,234.5678 rounded to the nearest hundred is 1,200. Choose a fraction when you work with measurements, such as the nearest 1/16 of an inch. The answer is shown with the denominator you picked, so 3.14159 to the nearest 1/16 reads 3 2/16, which is 3 1/8 once you reduce it. If you need to simplify the fraction, the Fraction Calculator will do it for you.
Rounding shows up whenever a calculator hands you more digits than you need. For money, round to hundredths in the Tip Calculator or Sales Tax Calculator. For a result in a science lab, you may need significant figures instead of decimal places, which is easier to see after converting to scientific notation. And to judge how much a rounded figure differs from the original, the Percent Error Calculator gives the exact size of the error.
Look at the digit just after the place you are rounding to. If it is 5 or more, round up. If it is less than 5, round down. This is the default rule for most schoolwork.
Half up always sends a tie upward (2.5 becomes 3, 3.5 becomes 4). Half to even sends a tie to the nearest even number (2.5 becomes 2, 3.5 becomes 4), which avoids a systematic upward bias.
Pick tens or hundreds in the precision menu. For example, 1,234.5678 rounded to the nearest hundred is 1,200.
It depends on the mode. The default sends −2.5 to −3 (away from zero), half up sends it to −2, and floor sends −2.6 to −3. The mode table shows every result.
Truncating just cuts digits off, which always moves the number toward zero. Rounding picks the nearest value at the chosen place.
Pick another tool to jump straight to it.
Convert numbers and round to significant figures.
LiveSimplify and calculate with fractions.
LiveSee how far a rounded value is from the true one.
LiveWork out percentages and percentage change.