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CalcChef

Rounding Calculator

Round a number to decimal places, significant figures, a whole number, a ten or hundred, or a multiple such as 5 or 0.25: 123.456789 to 2 places is 123.46. How it works

Use the Rounding Calculator

Fixed Decimal (2)
123.46
Significant Figures (2)
1.2e+2
Nearest Integer
123
Floor (Down)
123
Ceil (Up)
124

About the Rounding Calculator

123.456789 rounded to 2 decimal places is 123.46, and to 2 significant figures it is 120, shown as 1.2e+2. The rounding calculator takes a number and one precision and shows five results together: decimal places, significant figures, the nearest whole number, rounded down and rounded up. Switch Round to to tens, hundreds, thousands or millions and 12345 rounds to 12350, 12300, 12000 or 0; pick A multiple and 23 rounds to the nearest 5 as 25.

Rounding at a precision of 2

Number2 decimal places2 significant figuresNearest whole numberRounded downRounded up
3.141593.143.1334
0.1250.130.13001
1.0051.001.0112
2.6752.672.7323
-2.5-2.50-2.5-2-3-2
19.99920.0020201920
0.04560.050.046001
12501250.001.3e+3125012501250

As the tool shows them with the precision set to 2. 1.005 and 2.675 round down because the computer stores them slightly below the half.

How to use this tool

  1. Type the number.
  2. Set the precision: the number of decimal places, which is also the number of significant figures. 1 rounds to the nearest tenth, 2 to the nearest hundredth.
  3. The results update as you change a value.

Frequently asked questions

How do I round to 2 decimal places?
Look at the third decimal: 5 or more rounds the second one up, less leaves it. 3.14159 becomes 3.14 and 0.0456 becomes 0.05. With the precision at 2 the Fixed Decimal result keeps trailing zeros, so 19.999 shows as 20.00.
How do I round to the nearest 5, ten, hundred or thousand?
Pick Tens, Hundreds, Thousands or Millions under Round to. 12345 to the nearest ten is 12350, to the nearest hundred 12300 and to the nearest thousand 12000. A number exactly halfway goes away from zero, so 25 becomes 30 and -25 becomes -30. The page also shows the multiples below and above: 12345 rounded down to hundreds is 12300 and rounded up is 12400. For any other step pick A multiple: 23 to the nearest 5 is 25 and 1.37 to the nearest 0.25 is 1.25.
Why does 1.005 round to 1.00 and not 1.01?
The computer stores 1.005 as a binary number a little below 1.005, so it rounds down. 2.675 gives 2.67 for the same reason, while 0.125, which is stored exactly, rounds up to 0.13. A multiple works on the digits you typed, so 1.005 to the nearest 0.01 is 1.01, and the sig fig calculator does the same for significant figures.
What does 1.2e+2 mean in the result?
It is exponent notation for 1.2 × 10², which is 120. The Significant Figures row switches to it when the number has more whole-number digits than the precision: 1250 to 2 figures shows 1.3e+3, which is 1300.
How are halves like 2.5 rounded?
The nearest-whole-number result sends halves toward positive infinity: 2.5 becomes 3 and -2.5 becomes -2. The Fixed Decimal result rounds halves away from zero, so -2.5 at precision 0 shows -3 there. There is no round-half-to-even (banker’s rounding) option.
Can it round up or down to a number of decimals?
Yes, with A multiple: a multiple of 0.01 rounds 2.675 down to 2.67 and up to 2.68. With Round to set to decimal places, rounded down and rounded up always go to a whole number, whatever the precision, so 2.675 gives 2 and 3. With Round to set to a place value they go to that multiple, so 12345 rounded up to thousands is 13000.

Five ways to round one number

With the default 123.456789 and a precision of 2 it returns 123.46 to two decimal places, 1.2e+2 to two significant figures, which is 120, 123 to the nearest whole number, 123 rounded down and 124 rounded up. Set the precision to 1 for the nearest tenth and 2 for the nearest hundredth: 3.14159 becomes 3.1 and 3.14. Significant figures matter for small numbers: 0.000123456 is 0.000 to three decimals but 0.000123 to three significant figures.

Nearest, down and up go to a whole number, so 7.45 rounded down is 7. Under Round to, pick tens to millions (12345 becomes 12350, 12300, 12000 and 0) or A multiple for a step such as 5, 0.25 or 0.01.

How each result is produced

Decimal places use toFixed(p) and significant figures toPrecision(p), which switches to exponent form when the whole part has more digits than p (98765 to 3 is 9.88e+4). Nearest is Math.round, which sends halves toward positive infinity (2.5 → 3, −2.5 → −2); down and up are Math.floor and Math.ceil. The decimal results round a half away from zero, so −2.5 at precision 0 shows −3 in Fixed Decimal. These methods work on the stored binary value: 1.005 to two decimals gives 1.00 and 2.675 gives 2.67, because both are stored just below the half.

A multiple is worked on the digits you typed: multiple × round(x ÷ multiple), a tie going away from zero. 23 to the nearest 5 is 25, 1.37 to the nearest 0.25 is 1.25 (up is 1.5), −25 to the nearest 10 is −30, and 1.005 to the nearest 0.01 is 1.01. Round down and up give the multiples below and above, and a Working line shows 5 × round(23 ÷ 5) = 5 × 5. There is no half-to-even option and no truncation.

Fun Fact: The default rounding mode of the IEEE 754 floating-point standard is round half to even, which sends 2.5 to 2 and 3.5 to 4 so that rounding errors do not build up in one direction.

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