🔢 Antilog Calculator
By ToolNimba Math Team · Updated 2026-06-19
The antilog is the inverse of a logarithm: if log base b of y is x, then the antilog base b of x is y = b^x.
The antilog (antilogarithm) is the inverse of a logarithm. If you know the log of a number and want the number back, you take the antilog. For a base b and a value x, the antilog is simply b raised to the power x, written b^x. Enter the value x and a base (10 by default, but e or 2 are common too) and this calculator returns b^x at once, along with the natural antilog e^x and the binary antilog 2^x for comparison.
What is the Antilog Calculator?
A logarithm answers the question: to what power must I raise the base to get this number? The antilogarithm reverses that. If log base b of y equals x, then the antilog base b of x equals y, and y is found by computing b^x. In short, taking the log and taking the antilog undo each other, so antilog base b of (log base b of y) gives back y.
The most common case is base 10, the common logarithm. Antilog base 10 of x means 10^x. For example, since log base 10 of 1000 is 3, the antilog base 10 of 3 is 10^3 = 1000. The natural antilog uses base e (about 2.71828), so the antilog of x is e^x, the exponential function that appears throughout growth, decay and compound-interest problems. Base 2 is the binary antilog, 2^x, which shows up in computing and information theory.
Because the antilog is just exponentiation, the value x can be any real number, positive, negative or zero. A negative exponent gives a value between 0 and 1 (for a base greater than 1), since b raised to a negative power is one divided by b to the positive power. An exponent of 0 always gives 1, because any nonzero base raised to the power 0 equals 1. The base itself must be greater than 0, a base of zero or a negative number does not define a well-behaved antilog.
When to use it
- Reversing a logarithm in a physics, chemistry or engineering calculation to recover the original quantity.
- Converting a pH value back to hydrogen-ion concentration, where concentration = antilog of (negative pH).
- Working with decibels, Richter magnitudes or other log scales where you need the underlying linear value.
- Checking homework: confirming that the antilog of a log returns the number you started with.
How to use the Antilog Calculator
- Enter the value x, the exponent or log value you want to convert back.
- Enter the base b, or tap a quick button for base 10, base e, or base 2.
- Read the main result b^x, plus the natural antilog e^x and binary antilog 2^x.
- Try a negative or fractional x to see how the antilog behaves across the range.
Formula & method
Worked examples
Find the antilog base 10 of 2.5.
- The antilog base 10 of x is 10^x.
- Here x = 2.5, so compute 10^2.5.
- 10^2.5 = 10^2 × 10^0.5 = 100 × 3.162278
- 100 × 3.162278 = 316.2278
Result: antilog base 10 of 2.5 ≈ 316.2278
Find the natural antilog (base e) of -1.
- The natural antilog of x is e^x.
- Here x = -1, so compute e^(-1).
- e^(-1) = 1 ÷ e = 1 ÷ 2.718282
- 1 ÷ 2.718282 = 0.367879
Result: antilog base e of -1 ≈ 0.367879
Common antilog values for base 10 (10^x)
| x | antilog base 10 = 10^x |
|---|---|
| -2 | 0.01 |
| -1 | 0.1 |
| 0 | 1 |
| 0.5 | 3.162278 |
| 1 | 10 |
| 2 | 100 |
| 3 | 1000 |
Antilog of x = 1 across common bases
| Base b | antilog base b of 1 = b^1 |
|---|---|
| 2 | 2 |
| e (≈ 2.71828) | 2.718282 |
| 10 | 10 |
Common mistakes to avoid
- Mixing up the base of the antilog and the log. The antilog must use the same base as the logarithm you are reversing. The antilog base 10 of (log base e of y) does not return y. Match the base, or the round trip fails.
- Assuming antilog means natural exponent. Unless a base is stated, antilog usually means base 10 (10^x), not e^x. In many textbooks "antilog" alone is the common antilog. Check which base your problem expects.
- Thinking a negative x is invalid. The value x can be negative, zero or fractional. A negative exponent gives a small positive result between 0 and 1 for a base above 1, never a negative number or an error.
- Confusing antilog with reciprocal. The antilog of x is b^x, not 1 ÷ log(x) or 1 ÷ x. It is the inverse operation of taking a logarithm, which is exponentiation, not a reciprocal.
Glossary
- Antilogarithm
- The inverse of a logarithm. The antilog base b of x is b raised to the power x, written b^x.
- Logarithm
- The exponent to which a base must be raised to produce a given number. Antilog reverses it.
- Base
- The number that is raised to a power. Common bases are 10 (common), e (natural) and 2 (binary).
- Common antilog
- The antilog using base 10, equal to 10^x. Often what "antilog" means with no base stated.
- Natural antilog
- The antilog using base e (about 2.71828), equal to e^x, the exponential function.
Frequently asked questions
What is an antilog?
An antilog (antilogarithm) is the inverse of a logarithm. If log base b of y is x, then the antilog base b of x is y, found by computing b^x. Taking a log and then its antilog returns the original number.
How do you calculate the antilog of a number?
Raise the base to the power of the number. The antilog base b of x is b^x. For the common antilog, antilog(x) = 10^x, and for the natural antilog, antilog(x) = e^x. This calculator does it instantly for any base above 0.
What is the antilog of 2?
In base 10 the antilog of 2 is 10^2 = 100. In base e it is e^2 ≈ 7.389056, and in base 2 it is 2^2 = 4. The answer depends entirely on which base you use.
Is antilog the same as exponent?
Yes. Taking the antilog of x means computing b^x, which is exponentiation with the base b. Antilog is just the name used when you are reversing a logarithm rather than starting a fresh power calculation.
Can the antilog of a negative number be found?
Yes. The value x can be negative. For a base greater than 1, a negative x gives a positive result between 0 and 1, since b^(-x) equals 1 divided by b^x. For example, 10^(-2) = 0.01.
What base does antilog use by default?
When no base is given, antilog usually means the common antilog, base 10, so antilog(x) = 10^x. This calculator defaults to base 10 but lets you switch to base e or base 2, or type any base above 0.