Antilog Calculator
The antilog of 3 in base 10 is 1,000, because 10 raised to the power 3 is 1,000. This antilog calculator reverses a logarithm, raising the base to your number. It handles the common base 10, the natural base e, base 2, or any custom base you type in, and it accepts negative and decimal inputs.
Quick answer
A logarithm asks what exponent produces a number. The antilog runs that in reverse, applying the exponent.
Antilog
1,000
What this tells you
- •A logarithm asks what exponent produces a number. The antilog runs that in reverse, applying the exponent.
- •Antilog of x in base b is simply b to the power x.
- •Antilog base 10 of 2 is 100, of 3 is 1000, of -2 is 0.01.
- •Taking the antilog of a log returns the original number, which is how you undo a log transform.
How to Use
- 1Enter the number whose antilog you want, usually a log value you are reversing.
- 2Enter the base. Use 10 for common logs, 2.71828 for natural logs, or 2 for binary logs.
- 3Read the antilog as the main result.
- 4Very large or small results switch to scientific notation automatically.
How It Works
Formula
antilog_b(x) = b^xRaise the base to the power of your value. The antilog base 10 of 2.5 is 10^2.5, about 316.23. Negative inputs give values below 1, since 10^-2 is 1/100 = 0.01. Decimals work the same way. This is exactly how log tables were used in reverse before calculators: find the log, do the easy addition, then take the antilog.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Antilog of 3, base 10
10 x 10 x 10 = 1,000.
Antilog of 2.5, base 10
10^2.5 sits between 10^2 = 100 and 10^3 = 1000, at 316.23.
Antilog of 1, base e
e^1 is e itself, the natural antilog of 1.
Base 10 Antilog Table
Common log values and their base 10 antilogs.
| x | antilog(x) |
|---|---|
| -2 | 0.01 |
| -1 | 0.1 |
| 0 | 1 |
| 0.5 | 3.1623 |
| 1 | 10 |
| 2 | 100 |
| 3 | 1000 |
| 6 | 1000000 |
Common mistakes
- Using the wrong base. The antilog of 3 is 1000 in base 10 but only 8 in base 2. The base must match the log you are reversing.
- Confusing antilog with the reciprocal of a log. Antilog(x) is b^x, not 1/log(x).
- Dropping the sign. Antilog of -2 in base 10 is 0.01, not -100. Negative exponents shrink the result, they do not negate it.