About the Antilog Calculator
This antilog calculator finds the antilogarithm — the inverse of a logarithm — of a number in base 10, base e, base 2 or any positive base you choose. If log₁₀(y) = 2.5, the antilog of 2.5 is y = 10^2.5 ≈ 316.23. In general the antilog of x in base b is simply b raised to the power x.
It is handy for chemistry (turning pH or pKa back into concentrations), acoustics (decibels back to intensity ratios), seismology (Richter magnitudes), finance and statistics (back-transforming log-scale data), and for students who learned with printed log and antilog tables. For base 10 it also splits x into its characteristic (integer part) and mantissa (decimal part), the way antilog tables are used.
Results are shown as an ordinary number and in scientific notation, and the calculator checks the answer by taking the logarithm again. Negative inputs are fine — the antilog of −3 in base 10 is 0.001 — but the base must be positive and not equal to 1.
With the default inputs, the antilog (bˣ) is 316.2277660168. Change any value above to recalculate instantly.
How to use the antilog calculator
- 1Enter the number x — the logarithm you want to reverse.
- 2Choose the base: 10 for log, e for ln, 2 for binary, or a custom base.
- 3Read the antilog and its scientific notation.
- 4For base 10, use the characteristic and mantissa to follow the log-table method.
Formula and method
The antilogarithm undoes a logarithm: if log_b(y) = x, then y = bˣ. For the common logarithm (base 10) the antilog of x is 10ˣ; for the natural logarithm (base e ≈ 2.71828) it is eˣ, often written exp(x).
Printed antilog tables use base 10 and split x into an integer characteristic and a decimal mantissa between 0 and 1. The table gives 10^mantissa, a number between 1 and 10, and the characteristic tells you where to put the decimal point. For any other base, bˣ = 10^(x·log₁₀ b), which is how the base-10 characteristic and mantissa are shown for every base.
- b
- Base of the logarithm (10, e, 2 or custom)
- x
- The logarithm whose antilog you want
- characteristic
- Integer part of the base-10 logarithm
- mantissa
- Decimal part (0 ≤ m < 1) of the base-10 logarithm
Worked examples
Antilog of 2.5 (base 10)
10^2.5 = 10² × 10^0.5 = 100 × 3.16228 ≈ 316.23. The characteristic 2 places the decimal point after three digits, and the mantissa 0.5 gives the significant figures 3.16228.
Natural antilog of 1
The inverse of ln is the exponential function, so the natural antilog of 1 is e¹ ≈ 2.71828.
pH 3.7 to hydrogen-ion concentration
Since pH = −log₁₀[H⁺], [H⁺] = 10^−3.7 ≈ 1.995 × 10⁻⁴ mol/L. In table form, −3.7 = −4 + 0.3: antilog(0.3) ≈ 1.995 and the characteristic −4 shifts it to 0.0001995.
Base 2 antilog of 10
2¹⁰ = 1,024. Its base-10 logarithm is 10 × log₁₀ 2 ≈ 3.0103, so the characteristic is 3 — the number has four digits.
Frequently asked questions
What is an antilog?+
An antilog (antilogarithm) is the number whose logarithm is a given value. If log₁₀(1000) = 3, then antilog(3) = 1000. Mathematically, the antilog of x in base b is just b to the power x.
How do I calculate an antilog on a calculator?+
For base 10 press the 10ˣ key (often SHIFT + log) and enter the number. For natural logs use eˣ (SHIFT + ln). For another base b, compute b^x with the power key (xʸ or ^).
What is the antilog of a negative number?+
It is a positive number less than 1 (for bases greater than 1). For example the base-10 antilog of −2 is 10⁻² = 0.01. Antilogs are never negative or zero.
How do you use an antilog table?+
Write the logarithm as a characteristic (integer) plus a positive mantissa, e.g. −2.6 = −3 + 0.4. Look up the mantissa in the antilog table (antilog 0.4 ≈ 2.512), then multiply by 10 to the characteristic: 2.512 × 10⁻³ = 0.002512.
Is antilog the same as exponential?+
Yes. The natural antilog is the exponential function eˣ, and the base-10 antilog is 10ˣ. "Antilog" is the traditional name used with log tables; "exponential" is the modern term.