Rounding Calculator: Decimals, Places and Multiples

How to use the calculator

Enter the number. Negatives, grouping commas (1,234,567.891) and e-notation (1e-7) are accepted.
Choose what to round to: a place value from thousands to ten-thousandths, a number of decimal places (0–30), or the nearest multiple of any positive step, such as 0.05, 0.25, 5 or 100.
Pick a rounding mode. The default, half up, is the rounding taught in school.
Read the results. You get the rounded value, the increment used and the exact change from your original number. The table repeats the rounding under every mode.

How the rounding works

First the calculator turns your choice into an increment: hundredths is 0.01, 3 decimal places is 0.001, a multiple is the step itself. It divides the number's absolute value by the increment, rounds that quotient to a whole number with the chosen mode, multiplies back and restores the sign. All of this is done on the decimal digits as typed, with exact integer arithmetic and no binary floating point.

The modes differ in what they do with a tie (exactly halfway) or with the sign:

Mode	Rule	2.5	−2.5	−2.1
Half up	ties away from zero	3	−3	−2
Half even (banker's)	ties to the even neighbor	2	−2	−2
Half down	ties toward zero	2	−2	−2
Up (ceiling)	toward +∞	3	−2	−2
Down (floor)	toward −∞	2	−3	−3
Toward zero	truncate	2	−2	−2
Away from zero	any remainder rounds outward	3	−3	−3

All values are rounded to the ones place. A negative number that rounds to zero loses its sign: −0.001 to the hundredths shows 0.00, never −0.00.

Worked examples

1. 2.675 to the hundredths

Half up gives 2.68, a change of +0.005. JavaScript's (2.675).toFixed(2) returns "2.67", because 2.675 can't be stored exactly in binary floating point. The same happens with 1.005: the calculator gives 1.01, toFixed(2) gives "1.00". Banker's rounding sends ties to the even neighbor, so 2.665 becomes 2.66 while 2.675 still becomes 2.68.

2. Rounding to the nearest multiple

Number	Multiple	Half up	Up (ceiling)
4.67	0.05	4.65	4.70
2.68	0.05	2.70	2.70
7.38	0.25	7.50	7.50
23	5	25	25
12,345	100	12,300	12,400

Results keep as many decimals as the increment, so 2.68 to the nearest 0.05 shows 2.70.

3. A large number to the thousands

1,234,567.891 rounds to 1,235,000 (+432.109) under half up. Floor and toward zero give 1,234,000.

Choosing a mode

Half up matches most homework. Half even sends each tie to the even neighbor, so in a long list of values ending in 5 the ties are not all rounded in the same direction. Ceiling fits questions like "how many boxes do I need?", and floor or truncation fits "how many full units fit?". If a teacher, standard or program specifies a mode, use that one.

Frequently asked questions

Why does 2.675 round to 2.67 in some apps?

Many programs store decimals in binary floating point, where 2.675 is held as a value slightly below 2.675, so it rounds down. MDN documents this for JavaScript's toFixed(), with (2.55).toFixed(1) giving "2.5". This calculator rounds the digits you typed, so a true tie is treated as a tie.

What is banker's rounding?

It is round-half-to-even: a value exactly halfway goes to the neighbor whose last digit is even. 2.5 becomes 2, 3.5 becomes 4, and 2.665 to the hundredths becomes 2.66. Values that aren't ties round normally, so 2.6651 still becomes 2.67.

How do you round negative numbers?

In school rounding, −2.5 rounds to −3: ties go away from zero, mirroring 2.5 → 3. JavaScript's Math.round() is different. MDN notes it rounds a fraction of exactly 0.5 toward +∞, so −2.5 gives −2, which matches none of the tie modes here for negatives. Floor and ceiling also behave differently below zero: −2.1 floors to −3 but ceils to −2.

Is "round up" the same as "round half up"?

No. Half up only decides ties; 2.1 still goes to 2. Up (ceiling) moves any non-integer toward +∞, so 2.1 goes to 3. Watch the naming in code: Python's decimal module uses ROUND_UP for away from zero and ROUND_DOWN for toward zero. Here those are "Away from zero" and "Toward zero", while "Up" and "Down" mean ceiling and floor.

How do I round to the nearest 5, 10 or 0.05?

Choose "Nearest multiple" and enter the step: 5, 10, 0.05 or any positive number. For tens, hundreds and thousands you can also use the place value list.

Is rounding to decimal places the same as significant figures?

No. Decimal places fix the position of the last digit; significant figures count digits from the first nonzero one. 0.004050 to 2 decimal places is 0.00, but to 2 significant figures it is 0.0041. For significant figures, use the sig fig calculator.

Sources

This calculator rounds numbers for learning and everyday use. Where a teacher, contract, standard or software sets a specific rounding rule, that rule applies.