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Antilog Calculator
Use this free antilog calculator to find the antilog of any number — base 10, base 2, base e, or your own custom base. Antilog is simply the inverse of a logarithm: if the log of a number is x, the antilog of x gives the number back. Students use it with log tables for long multiplication, and scientists use it for pH, decibels and earthquake scales. Type a number and the answer appears as you type, with no sign-up.
How to use this calculator
- Choose the base: 10 for ordinary antilog, 2 or e for binary and natural work, or Custom for anything else and type the base.
- Type the number whose antilog you want — the log value — for example 2.5.
- Read the answer in the result box. It updates as you type, and the line below shows the power that was calculated.
- To check a log answer, feed the result into a log calculator: the log of 316.2278 comes back as 2.5.
Common antilog values (base 10)
| Number (x) | Antilog = 10x |
|---|---|
| 0.5 | 3.1623 |
| 1 | 10 |
| 1.5 | 31.6228 |
| 2 | 100 |
| 2.5 | 316.2278 |
| 3 | 1,000 |
How it works
A logarithm answers the question: "to what power must I raise the base to get this number?" Antilog asks the same question backwards. If log10(y) = x, then the antilog of x is y, and the way to compute it is simply antilog(x) = 10x. For any other base b, antilogb(x) = bx. That is all this calculator does — it raises the base to your number — but it saves the slow part, because powers like 10^2.5 are not ones you can do in your head.
The classic school method uses a four-figure antilog table, and it is worth understanding because exams still test it. Split the number into the characteristic (the whole part, here 2) and the mantissa (the decimal part, here .5). The antilog table gives the digits for the mantissa: antilog of .5 is 3.162. The characteristic then tells you where the decimal point goes — characteristic 2 means the answer has 3 digits before the point — giving 316.2, very close to the exact 316.2278 that this calculator shows.
Negative inputs are fine too. Antilog of −1 is 10−1 = 0.1, and antilog of −2.5 is about 0.003162. The result of an antilog is always positive, because a positive base raised to any power — whole, fractional or negative — is always positive. That is also why pH works: a pH of 4.5 becomes a hydrogen-ion concentration of antilog(−4.5) ≈ 0.0000316.
One caution about bases: the base must be a positive number other than 1. Base 1 breaks because 1 to any power is always 1, so it has no inverse; negative bases give results that jump between positive and negative and are not used for antilog. Bases 10 and e cover almost all school and science work, and base 2 appears in computing.
Worked example
A chemistry student finds that the log of a concentration is 2.5 and needs the actual number — the antilog of 2.5.
Step 1: Identify the base — the common log, base 10.
Step 2: Split the power — 102.5 = 102 × 100.5.
Step 3: Work out each part — 102 = 100, and 100.5 = 3.16228 (the square root of 10).
Step 4: Multiply — 100 × 3.16228 = 316.228, which rounds to 316.2278.
The log-table method agrees: the mantissa .5 gives digits 3.162 and the characteristic 2 places the point after three digits, so 316.2. The calculator's exact answer is 316.2278 — the exact result this page gives for base 10 and 2.5.
FAQ
What is the antilog of 2.5?
The antilog of 2.5 (base 10) is 316.2278. Antilog undoes a logarithm: since log of 316.2278 is 2.5, the antilog of 2.5 is 10 raised to the power 2.5, which is 316.2278.
What is the difference between log and antilog?
Log and antilog are opposites. The log of a number is the power you must raise the base to in order to get that number; the antilog takes that power and gives the number back. log(1000) = 3, and antilog(3) = 1000.
How do I find the antilog using a log table?
Split the number into its whole part (characteristic) and decimal part (mantissa). For 2.5, the mantissa is .5: look up the antilog of .5 in the antilog table to get 3.162, then use the characteristic 2 to place the decimal point two steps up — 316.2, close to the exact 316.2278.
Can the antilog be taken with bases other than 10?
Yes. This calculator offers base 10, base 2, base e and any custom base. For example, antilog base 2 of 10 is 2^10 = 1,024, and antilog base e of 3 is e^3 = 20.0855. The base must be positive and not equal to 1.
What is the antilog of a negative number?
It is a small positive decimal, never negative. Antilog of −1 (base 10) is 10^−1 = 0.1, and antilog of −2 is 0.01. Powers of a positive base are always positive, so an antilog can never be zero or negative.
Where is antilog used in real life?
Chemists use it to turn pH back into hydrogen-ion concentration, engineers use it with decibels and the Richter scale, and it appears in compound growth, electronics and signal processing — anywhere a log scale has to be converted back into a real quantity.