Determine Magnitude of a Number

Calculator for the magnitude of a very large or very small number. The order of magnitude indicates in which range of powers of ten a number lies. This results from the position of the first digit of a number greater than or equal to one, or the position of the first digit after the decimal point not equal to zero in the case of a number less than one. The number itself is irrelevant. A sign is ignored. Please enter a number, the magnitude of this number is displayed up to 65 digits, this number is called hundred vigintillion.

Examples: the number 123456789 is in the magnitude of hundred million, as is the number 987654321. This is because both have the same amount of digits. 0.000000005 is in the magnitude of billionth.

The order of magnitude is particularly important for values with low precision and those that can change significantly. Low precision arises, for example, in estimations when a quantity is difficult to count, perhaps because not all parts can be observed or there are simply too many, and only a rough estimate is possible. Therefore, when dealing with such an uncertain value, the order of magnitude, which is basically also just a rounding, can provide more information about the true value than an exact but likely incorrect number. This is because the order of magnitude also conveys information about the accuracy. If the expected error exceeds a factor of 10, meaning the true value could be more than ten times or less than one-tenth of the calculated value, this should be specified. Otherwise, the order of magnitude will give a false impression of a too high precision.

For the rounding mith magnitudes, see Fermi rounding. To display not only the order of magnitude, but the exact name of large numbers, see Numerals Calculator.

Number:
Power of ten:
Magnitude: