Math
Antilog Calculator
The antilog undoes a logarithm: if log_b(x) = y, then antilog_b(y) = b^y = x.
Enter the log value and the base to recover the original number, exactly when the exponent is a whole number, with scientific notation for very large or small results.
The logarithm you want to undo. Can be negative or a decimal.
Try an example
Result
Antilog b^y
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- Expression
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What an antilog is
Antilog is short for antilogarithm, the inverse operation of a The exponent you would need to raise a base to in order to get a number.. Taking a log turns a number into an The small raised number saying how many times to multiply the base by itself.; taking the antilog turns the exponent back into the number. On a scientific calculator it is the 10^x key (for common logs) or the e^x key (for natural logs).
Common antilog values
| Log value y | antilog₁₀(y) = 10^y | antilog_e(y) = e^y | antilog₂(y) = 2^y |
|---|---|---|---|
| -1 | 0.1 | 0.3679 | 0.5 |
| 0 | 1 | 1 | 1 |
| 0.5 | 3.1623 | 1.6487 | 1.4142 |
| 1 | 10 | 2.7183 | 2 |
| 2 | 100 | 7.3891 | 4 |
| 3 | 1,000 | 20.0855 | 8 |
Where antilogs are used
- pH: hydrogen ion concentration [H⁺] = 10^(-pH).
- Decibels: power ratio = 10^(dB / 10).
- Richter scale: amplitude ratio between magnitudes m₁ and m₂ is 10^(m₁ - m₂).
- Undoing a log-transformed regression or a log scale on a chart.
How to use it
- Pick the The number being raised to a power, or the side a shape's height is measured from. that matches the logarithm you are undoing: 10 for log, e for ln, 2 for log₂, or custom.
- Enter the log value y.
- Read b^y. Whole-number exponents give an exact value; decimals give a precise approximation plus Writing a number as one digit, a decimal part, and a power of ten..
How to read the answer
The antilog is the original number before the logarithm was taken. antilog₁₀(3) = 1000 because log₁₀(1000) = 3. Negative log values give numbers between 0 and 1.
Common mistakes and edge cases
- Using base 10 to undo a natural log. ln needs base e.
- Reading a negative antilog: b^y is always positive for a positive base.
- Confusing antilog with 1/log(x). The antilog is an exponential, not a The number you get by flipping a fraction; 3/4 becomes 4/3, and 5 becomes 1/5..
Worked examples
Common antilog
antilog₁₀(3) = 10^3
Antilog b^y
1,000
Natural antilog
antilog_e(2) = e^2
Antilog b^y
7.3890561
Negative log value
antilog₁₀(-2) = 0.01
Antilog b^y
0.01
Decimal log value
antilog₁₀(2.5)
Antilog b^y
316.22776602
Binary antilog
antilog₂(10) = 1024
Antilog b^y
1,024
Custom base
antilog₅(3) = 125
Antilog b^y
125
pH 7.4
[H⁺] = 10^-7.4
Antilog b^y
0.00000004
Invalid base
Base 1 has no logarithm
Antilog b^y
Error
Frequently asked questions
How do I find the antilog of a number?+
Raise the base to that number. For a common log, antilog(y) = 10^y; for a natural log, e^y. On a calculator use the 10^x or e^x key, often the second function of the log or ln key.
What is the antilog of 3?+
For base 10, antilog(3) = 10^3 = 1,000. For base e it is e^3 ≈ 20.09, and for base 2 it is 2^3 = 8. Always check which base the log used.
Can an antilog be negative?+
No. For any positive base, b^y is positive. A negative log value just gives a result between 0 and 1.
What is the antilog of a negative number?+
A fraction: antilog₁₀(-2) = 10^-2 = 0.01. Negative exponents mean reciprocals.
Is antilog the same as inverse log?+
Yes. Antilog, inverse log, and exponentiation with the same base all describe the same operation.
How is antilog used for pH?+
pH = -log₁₀[H⁺], so [H⁺] = 10^(-pH). For pH 7.4, [H⁺] = 10^-7.4 ≈ 3.98 × 10^-8 mol/L.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026