Rounding Calculator

This rounding calculator handles every common rule in one place: round to the nearest tenth, hundredth, thousandth, whole number, or to a chosen number of significant figures. Type a value, pick a target place, and you get the standard result plus the ceiling and floor so you can see which direction each method pushes the answer.

1. Enter the number you want to round.It can be a decimal like 3.14159, a small value like 0.00543, or an integer like 12345. Negative numbers work too, and signs change which direction counts as "up".
2. Choose the target place. Move the slider from 0 to 10 decimal places. 0 gives a whole number, 1 rounds to the nearest tenth, 2 rounds to the nearest hundredth, 3 rounds to the nearest thousandth, and so on.
3. Pick a rounding method. The main result uses round half up, the rule taught in most schools. Ceiling always moves toward positive infinity, floor always moves toward negative infinity. The comparison table below the result shows all three side by side at every precision level from 0 up to your chosen place.
4. Check significant figures. The sig fig grid shows the same number rounded to 1, 2, 3, 4, and 5 meaningful digits, which is what scientific and engineering work usually asks for instead of decimal places.

Use the comparison table to spot edge cases. Numbers that end in exactly 5 behave differently under each method, and negative numbers flip which method is "more" and which is "less". The table makes those differences obvious without having to recompute by hand.

There is no single rounding rule. Different fields picked different tie-breakers, and the method you choose can change totals by a few cents on a short column of numbers or by measurable amounts on long scientific tables. Here are the six you will run into most often, with real numbers for each.

Round half up (standard school rounding)

Look at the digit right after the cutoff. If it is 5 or more, round up. If it is 4 or less, round down. This is what most calculators and spreadsheets use by default and what students learn first.

2.5 → 3     (digit after cutoff is 5, round up)
2.4 → 2     (digit is 4, round down)
3.14559 to 2 dp → 3.15
3.14159 to 2 dp → 3.14

Round half to even (banker's rounding, IEEE 754 default)

When the dropped digit is exactly 5 with nothing meaningful after it, round to the nearest even number instead of always rounding up. On any single value it looks strange, but across a long column of sums it cancels out the upward bias that plain half-up introduces. This is the default in IEEE 754 floating point, the Python round() function, and most financial systems.

2.5 → 2     (2 is even, round down)
3.5 → 4     (4 is even, round up)
4.5 → 4     (4 is even)
5.5 → 6     (6 is even)
0.125 → 0.12 to 2 dp (2 is even)

Round half away from zero

Ties round to the larger magnitude, so positive halves go up and negative halves go down. This is what most people intuitively mean by "rounding", and it is what US tax forms and many accounting standards use.

2.5  → 3
−2.5 → −3
7.5  → 8
−7.5 → −8

Round toward zero (truncation)

Drop the extra digits without looking at what comes after. This is the same as floor for positive numbers and ceiling for negative numbers. C and Java integer division truncate, which is why 7 / 2 gives 3 in those languages.

2.9  → 2
−2.9 → −2
7.999 → 7
−0.5 → 0

Floor (toward −∞) and Ceiling (toward +∞)

Floor always moves toward negative infinity, so it rounds positive numbers down and negative numbers more negative. Ceiling does the opposite. Use ceiling when you need enough of something (tiles, pages, shipping boxes) and floor when you cannot exceed a limit (budget caps, available seats).

floor(2.9)   = 2       ceiling(2.1)  = 3
floor(−2.1)  = −3      ceiling(−2.9) = −2
floor(7.0)   = 7       ceiling(7.0)  = 7

Decimal places vs significant figures

Decimal places count digits after the decimal point. Significant figures count meaningful digits starting from the first non-zero digit. For small numbers the two give very different answers.

0.001234 to 2 decimal places  = 0.00
0.001234 to 2 significant figures = 0.0012

12345 to 0 decimal places = 12345
12345 to 2 significant figures = 12000

3.14159 to 3 decimal places  = 3.142
3.14159 to 3 significant figures = 3.14

Quick-reference table

Here are eight tricky values run through each method so you can see exactly how they differ on ties and negatives.

Rounding looks trivial until a spreadsheet total is off by a penny or a scientific paper shows too many digits. The rule you apply, the order you apply it in, and the way the underlying hardware stores the number all matter. Here is what actually trips people up.

When banker's rounding matters vs when half-up matters

On a single value, half-up and half-to-even disagree only on exact halves, and the difference is at most one unit in the last place. On large columns of numbers the gap grows. Round 200 values that all end in .5 using half-up and every one rounds up, so the total is biased high by 100. Round the same column half-to-even and roughly half round down, so the bias is near zero. That is why bank reconciliation, tax tables, and IEEE 754 math default to half-to-even. For a worksheet of ten numbers, a receipt, or a classroom assignment, half-up is fine and easier to explain.

Floating-point rounding quirks

Computers store most decimals in binary, and 0.1, 0.2, and most "clean" decimals cannot be written exactly in binary. In JavaScript, Python, and any other IEEE 754 language you will see this:

0.1 + 0.2       = 0.30000000000000004
0.1 + 0.2 == 0.3 → false
(0.1 + 0.2).toFixed(2) = "0.30"
Math.round(2.5)  = 3   (JS, half away from zero)
round(2.5)       = 2   (Python 3, half to even)

The lesson: never compare floats with ==, always round to a known precision before displaying or comparing, and know which method your language uses. JavaScript's Math.round is half away from zero for positives and half toward zero for negatives, which surprises people coming from Python.

Significant figures vs decimal places

Scientific and engineering writing uses significant figures because they track how precise the measurement actually is. If you measure something as 0.00345 grams and report 0.00 grams because your spreadsheet rounds to 2 decimal places, you have thrown away the entire measurement. Money, by contrast, uses decimal places because the smallest unit is fixed: two for US dollars, zero for Japanese yen. Use sig figs when the scale of the number varies, use decimal places when the currency or unit fixes the scale.

Common traps: chaining rounds and premature rounding

Rounding twice is not the same as rounding once. Take 2.449. Round it to 2 decimal places and you get 2.45. Round that result to 1 decimal place and you get 2.5. Round the original 2.449 straight to 1 decimal place and you get 2.4. Two different answers from the same number. Always round from the full-precision value, not from an already-rounded intermediate. Same rule for multi-step formulas: keep every calculation at full precision and only round the final display value. Premature rounding in spreadsheets is the single most common cause of "off by a cent" bugs in invoices and payroll.