Antilog Calculator

Antilog (b^x) —

Base used: —
Scientific notation: —
Characteristic (power of 10): —
Mantissa (base-10 fraction): —
Reciprocal, b^(−x): —

The antilog reverses a logarithm: if log_b(y) = x, then y = b^x. For a common (base-10) log of 2.5, the antilog is 10^2.5 = 316.227766. Pick the base, type the log value, and the calculator returns the number along with its characteristic, mantissa and scientific-notation form.

About this tool

Students working from log tables, chemists turning pH back into hydrogen-ion concentration, and engineers converting decibel or Richter figures all need to undo a logarithm. This calculator raises the chosen base to the power you enter. It handles common logs (base 10), natural logs (base e), binary logs (base 2) and any other positive base apart from 1. Alongside the result it splits the base-10 exponent into the characteristic, which fixes the decimal point, and the mantissa, which fixes the digits, the same split a printed antilog table uses. It also gives the reciprocal, handy when the log was negative. Results are shown to ten significant figures, and anything beyond roughly 10^308 or below 10^-307 cannot be represented, so very large logarithms return an error instead of a value.

How to use it

Choose the base
Select Common (10), Natural (e), Binary (2), or Other base to type your own.
Enter a custom base if needed
With Other base selected, type any positive number except 1, for example 5 or 0.5.
Type the logarithm value
Enter x, the log you want to reverse; negative and decimal values are fine.
Read the result and working
The antilog appears with its scientific form, characteristic, mantissa and the steps that produced it.

Examples

Common antilog of 2.5

Logarithm base: Common (10)
Logarithm value x: 2.5

Result Antilog (b^x): 316.227766
Base used: 10
Scientific notation: 3.16227766 × 10^2
Characteristic (power of 10): 2
Mantissa (base-10 fraction): 0.5
Reciprocal, b^(−x): 0.00316227766

antilog_10(2.5) = 10^2.5
As a power of 10: 2.5 × log10(10) = 2.5
Characteristic = 2, mantissa = 0.5
10^0.5 = 3.16227766, so the antilog = 316.227766

Characteristic 2 places the decimal point; the mantissa 0.5 gives the digits 3.162277660, the square root of ten.

Natural antilog of 1

Logarithm base: Natural (e)
Logarithm value x: 1

Result Antilog (b^x): 2.718281828
Base used: e ≈ 2.718281828
Scientific notation: 2.718281828 × 10^0
Characteristic (power of 10): 0
Mantissa (base-10 fraction): 0.4342944819
Reciprocal, b^(−x): 0.3678794412

antilog_e(1) = e^1
As a power of 10: 1 × log10(e) = 0.4342944819
Characteristic = 0, mantissa = 0.4342944819
10^0.4342944819 = 2.718281828, so the antilog = 2.718281828

The natural antilog of 1 is e itself, which the tool shows to ten significant figures.

Binary antilog of 10

Logarithm base: Binary (2)
Logarithm value x: 10

Result Antilog (b^x): 1024
Base used: 2
Scientific notation: 1.024 × 10^3
Characteristic (power of 10): 3
Mantissa (base-10 fraction): 0.0102999566
Reciprocal, b^(−x): 0.0009765625

antilog_2(10) = 2^10
As a power of 10: 10 × log10(2) = 3.010299957
Characteristic = 3, mantissa = 0.0102999566
10^0.0102999566 = 1.024, so the antilog = 1024

2 to the 10th is 1024, the number of bytes in a kibibyte; as a power of ten it is 1.024 × 10^3.

How it is calculated

y = b^x = 10^(x · log10 b) = 10^m × 10^c

b: the base of the logarithm (10, e, 2 or custom)
x: the logarithm value being reversed
c: characteristic: the whole-number part of the base-10 exponent, rounded down
m: mantissa: the fractional part, between 0 and 1

The antilog is the exponential function of the chosen base. To show it the way log tables do, the exponent is first rewritten as a power of ten, x times log10 of b. Rounding that down gives the characteristic, which says where the decimal point goes; the leftover fraction is the mantissa, and 10 raised to the mantissa gives the significant digits between 1 and 10. For a negative log such as −2.3, the characteristic is −3 and the mantissa 0.7, matching the bar notation 3̄.7 used in older tables.

When not to use it

Do not use it to undo a log of a negative number; real logarithms are only defined for positive values.
Avoid it for exponents above about 308 in base 10, where the result overflows double precision.
Complex logarithms and branch choices are outside its scope.

Common mistakes

Using base 10 when the log came from ln on a calculator, which gives e^x instead of 10^x.
Treating a negative characteristic as negative digits; the mantissa stays positive.
Entering the pH itself instead of its negative when recovering hydrogen-ion concentration.

Frequently asked questions

What does antilog mean?

Antilog is short for antilogarithm, the inverse of a logarithm. If log base b of y equals x, then the antilog of x is y, found by raising b to the power x. For base 10, the antilog of 3 is 1000.

Is the natural antilog the same as e^x?

Yes. The natural logarithm uses base e, about 2.718281828, so its antilog is the exponential function e^x. The antilog of ln 5 returns 5, and the natural antilog of 1 is e itself.

How do I find the antilog of a negative number?

Enter the negative value directly. The antilog of a negative log is a positive number below 1: the common antilog of −3 is 0.001. The characteristic shown will be negative, while the mantissa stays between 0 and 1.

What are the characteristic and mantissa?

They split a base-10 exponent into a whole part and a fractional part. The characteristic, rounded down, tells you the power of ten and so the decimal point position. The mantissa gives the digits through 10 to that fraction. Printed antilog tables were indexed by the mantissa only.

How do I convert pH back to hydrogen-ion concentration?

Concentration in mol/L equals 10 to the power of minus pH. Choose the common base and type the negative of the pH, so pH 3.2 means entering −3.2, which gives about 0.000631 mol/L.

Why can the base not be 1?

One raised to any power is still 1, so a base-1 logarithm cannot distinguish numbers and is undefined. The base must also be positive, because a negative base raised to a fractional power has no real value.

Cite this tool

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APA

Tools Directory Editorial Team. (2026, October 26). Antilog Calculator. Tools Directory. Retrieved October 26, 2026, from https://tools.milunir.com/math/algebra-tools/antilog-calculator/

MLA

Tools Directory Editorial Team. “Antilog Calculator.” Tools Directory, 26 Oct. 2026, https://tools.milunir.com/math/algebra-tools/antilog-calculator/. Accessed 26 Oct. 2026.

Chicago

Tools Directory Editorial Team. “Antilog Calculator.” Tools Directory. Last modified October 26, 2026. Accessed October 26, 2026. https://tools.milunir.com/math/algebra-tools/antilog-calculator/.

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