Quick answer
The antilogarithm undoes a logarithm: antilog_b(y) = b^y. With base 10, the antilog of 3 is 1,000.
Enter a logarithm value and a base. The calculator returns b raised to that value.
Related tools: Slope Calculator: Slope, angle, distance and line equation through two points. LCM Calculator: Least common multiple of two or more numbers. Factor Calculator: List every factor of a positive whole number.
How to use the Antilog Calculator
- Enter logarithm value y.
- Enter base b (above 0). It starts at 10.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Logarithm value y | A number | — |
| Base b | A number | > 0, starts at 10 |
Formula and method
Formula
antilog_b(y) = b^y
IEEE-754 double precision; shown to at most 6 decimal places.
Exponentiation.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Logarithm value y = 3; Base b = 10.
| Result | Value |
|---|---|
| Antilog | 1,000 |
Example 2
Inputs: Logarithm value y = 5; Base b = 2.
| Result | Value |
|---|---|
| Antilog | 32 |
Example 3
Inputs: Logarithm value y = -2; Base b = 10.
| Result | Value |
|---|---|
| Antilog | 0.01 |
The first line is the headline result (antilog). IEEE-754 double precision; shown to at most 6 decimal places.
More worked cases
antilog₁₀(2) = 100, antilog₁₀(0.301) ≈ 2, and with base e (natural log) antilog(1) = e = 2.71828. In pH, [H⁺] = antilog(−pH), so pH 3 means 10⁻³ mol/L.
Where this estimate stops applying
The base must be positive and not 1. Very large exponents overflow and are reported. A negative exponent gives a fraction: antilog₁₀(−2) = 0.01.
Where antilogs are used
An antilog undoes a logarithm: antilog base 10 of 3 is 10³ = 1,000. In chemistry the hydrogen-ion concentration is the antilog of −pH, so a pH of 3 means 10⁻³ = 0.001 mol/L.
In acoustics and electronics a level in decibels converts back to a power ratio with 10^(dB ÷ 10), so 30 dB is a ratio of 1,000.
How the result changes with logarithm value y
Holding every other input at the first worked example, this table changes only logarithm value y. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Logarithm value y | Antilog |
|---|---|
| 1.5 | 31.622777 |
| 3 | 1,000 |
| 6 | 1,000,000 |
| 12 | 1,000,000,000,000 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Base b: entering "1" shows "The base must not be 1." beside that field and no result.
- Logarithm value y: entering "500" shows "The result is too large to represent." beside that field and no result.
Choosing between the Antilog Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Slope Calculator](/math/slope-calculator/) | x₁, y₁ and x₂ | Slope |
| [LCM Calculator](/math/lcm-calculator/) | numbers | Least common multiple |
| [Factor Calculator](/math/factor-calculator/) | number | Factors |
| [Quadratic Formula Calculator](/math/quadratic-formula-calculator/) | a, b and c | Roots |
| [Log Calculator](/math/log-calculator/) | number x and base b | log base 2 of 8 |
Background: algebra
Many algebra calculators rest on the same ideas: write the problem in a standard form, identify the coefficients, apply the formula and check the answer by substituting it back. For a quadratic ax² + bx + c = 0 the roots are (−b ± √(b² − 4ac)) ÷ 2a, and the discriminant b² − 4ac decides the kind of roots: positive gives two real roots, zero gives one repeated root and negative gives two complex conjugate roots.
If a = 0 the equation is linear, not quadratic. A sign slip on the −b term shifts both roots by the same amount, so substitute your roots back to check.
Assumptions and limitations
- Base must be positive and not 1
- Overflow is reported
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for base b and logarithm value y to confirm this.
Frequently asked questions
What is antilog of 2 in base 10?
The antilog of 2 in base 10 is 10² = 100.
How is it different from exp?
exp is the antilog in base e.
Where is it used?
Decibels, pH and Richter scales.
What is the antilog of 2 in base 10?
It is 10² = 100.
How do I undo a natural logarithm?
Use base e: the antilog of ln x is e raised to that value, so the antilog of 1 is e ≈ 2.71828.
What does the Antilog Calculator calculate?
Inverse logarithm: raise a base to a power. It returns Antilog.
What formula does the Antilog Calculator use?
antilog_b(y) = b^y. Exponentiation.
What do I need to enter in the antilog Calculator?
You enter Logarithm value y and Base b.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Base must be positive and not 1.
What are the limits of this calculator?
Base must be positive and not 1. Overflow is reported.
What is an example of a antilog result?
With logarithm value y 3 and base b 10, the antilog is 1,000.
Related calculators
- Slope Calculator — Slope, angle, distance and line equation through two points.
- LCM Calculator — Least common multiple of two or more numbers.
- Factor Calculator — List every factor of a positive whole number.
- Quadratic Formula Calculator — Solve ax² + bx + c = 0, including complex roots.
- Log Calculator — Logarithm of a number to any base.
- GCF Calculator — Greatest common factor (greatest common divisor) of two or more numbers.
- Prime Factorization Calculator — Break a whole number into its prime factors.
- Exponent Calculator — Raise a base to any power.
- Perfect Square Calculator — Check whether a number is a perfect square.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.