Antilog Calculator - Inverse Log Solver for Any Base

An antilog calculator is a math tool that reverses a logarithm. Given y and the base b that produced it, the calculator returns the original number x by computing b to the power of y. It is useful for students completing log-table homework, technicians converting dB and pH values back into linear or concentration units, scientists reading back-calculated exponential data, and anyone who needs to undo a logarithm without hunting for a printed antilog table.

• • Convert pH to hydrogen ion concentration: Recover the molar hydrogen ion concentration from a measured pH by computing 10 to the power of minus pH.
• • Turn a decibel reading into a power ratio: Recover the linear power or intensity ratio from a decibel value by raising 10 to the dB divided by 10, or to the dB divided by 20 for amplitude.
• • Finish a log-table calculation: Complete a multiplication, division, or root problem that started with a logarithm by taking the antilog of the final answer.
• • Solve a chemistry or rate equation: Recover a concentration, half-life, or rate-constant value when an equation reduces to b raised to a power.

The antilog operation is the second half of any calculation that started with a logarithm. The result is a positive number, no matter what the input y was, because a positive base raised to any real power is positive.

The output is a single number plus the same answer written as b to the power of y so you can confirm the calculation by hand.

For the long-form version of the same calculation, with a worked base-10 example and a characteristic-mantissa walkthrough, see our anti-logarithm calculator for the same math written out in a separate article.

The calculator reads y and the base b that produced it, then raises b to the power of y. The default base is 10 for a common log, but you can switch to the natural log base e or to any custom positive base such as 2 for a binary log.

• y (logarithm value): The logarithm value you want to invert. Accepts any finite real number including 0 and negative values.
• b (logarithm base): The base of the original logarithm. Defaults to 10, accepts e for the natural log, and any positive real number other than 1 when Custom is selected.
• x (antilogarithm): The result of raising b to the power of y. Always a positive real number when b is a positive real number.

For a common log the calculation is exactly 10 to the power of y. For a natural log the calculation is e to the power of y, where e is approximately 2.71828. For a custom base the same exponent rule applies, so a binary log of 10 inverts to 2 to the power of 10, which is 1024.

The result is shown two ways. The exponential form string repeats the calculation in the form b to the power of y equals result, so the user can verify the operation visually. The characteristic and mantissa of y are also returned to support the table-style read of any logarithm value.

According to Wolfram MathWorld, the antilogarithm is the inverse function of the logarithm, defined so that if log base b of x equals y, then the antilogarithm of y in base b is x = b to the power of y.

When you need to go in the opposite direction, take the log of a number with the log calculator and use this antilog calculator to invert the result back to the original value.

Four concepts make every antilog calculation easier to read, and they appear on any log-table or chemistry workbook that uses the same operation.

A negative y is fine, and a y of 0 always returns 1 because any positive base to the power of 0 equals 1. The result of an antilog is always a positive number, which is why the antilog is only defined for positive bases.

Characteristic and mantissa are the same components a log table uses to break a number into a magnitude and significant-digits part. Once you can read them, you can sanity-check any antilog result.

The base-to-the-power form in the formula is the same operation our exponent calculator handles for any exponent, so the antilog result can be cross-checked against a direct exponentiation for the same inputs.

The form takes the logarithm value, the base, and an optional custom base. The result updates as soon as any field changes.

1. 1 Enter the logarithm value: Type the y you want to invert into the Logarithm value field. Any finite real number, including negatives and zero, is accepted.
2. 2 Pick the base of the original log: Choose Common log for base 10, Natural log for base e, or Custom when the log was taken with another base.
3. 3 Enter a custom base if needed: When you pick Custom, type the original base into the Custom base field. The field accepts any positive real number other than 1.
4. 4 Read the antilog and the exponential form: The Antilogarithm field shows the numeric result and the Exponential form field shows the same answer written as b to the power of y.
5. 5 Use the characteristic and mantissa for sanity checks: Compare the characteristic and mantissa of y to the magnitude and significant digits of the antilog result to verify the calculation.

A laboratory notebook lists a pH of 4.7. To find the hydrogen ion concentration, enter y = minus 4.7, set the base to 10, and read the antilog. The calculator returns about 1.995 times 10 to the power of minus 5, the expected hydrogen ion concentration for a pH of 4.7 in mol per liter.

Once you have an antilog result, the scientific notation calculator reformats it as a coefficient times a power of ten, which is the standard way to read very small or very large antilog values in lab work.

The result tells you exactly which number the logarithm was hiding, and the exponential form tells you how the calculator reached it.

• • Direct inverse calculation: Recovers the original number from any log value in a single step, without searching through printed antilog tables.
• • Three built-in base options: Supports base 10, base e, and any custom positive base such as 2 for binary logs.
• • Negative value handling: Returns a positive fraction for negative y values, so pH and decibels can be inverted without a sign correction step.
• • Characteristic and mantissa breakdown: Returns the integer and fractional parts of y so the result can be read with the same magnitude and significant-digits logic a log table uses.
• • Visible exponential form: Prints the same answer in the form b to the power of y, so the user can verify the operation by eye.

Rerun the calculator whenever a new log value is generated. The output is reproducible because the formula is the same exponentiation regardless of the order of operations.

For batch work, copy the y values into a column and the bases into a second column, then run the calculation for each pair. The exponential form string is stable across the table.

A few characteristics of the input and the chosen base change the readability of the result, even when the underlying math is the same.

• • The calculator only handles a single logarithm value at a time. For batch conversions, copy the column of y values into a spreadsheet and apply the exponentiation to each row.
• • The result is rounded for display only. The internal value uses the full double-precision power, so chaining the antilog with a follow-up calculation should use the unrounded exponentiation rather than the displayed value.
• • The calculator does not handle complex logarithms. The y input must be a real number, and the chosen base must be a positive real number, because the antilog of a complex value is outside the scope of a standard log table.

When the input is a pH value, the input y is normally negative and the antilog is a very small concentration. When the input is a sound measurement in decibels, y is the dB value divided by 10 or 20 and the antilog is a linear power or amplitude ratio.

When the antilog is a googol-scale number, switch the result panel to scientific notation. The exponential form string always uses the same notation as the input.

According to Cuemath Antilog Table, the antilog of a number is found by raising 10 to that number, so antilog of 2 equals 100, antilog of minus 3 equals 0.001, and the characteristic plus mantissa split is the standard way to read any logarithm value before applying the antilog.

According to Wikipedia Logarithm article, the logarithm and the antilogarithm are inverse operations because the function log base b is the inverse of exponentiation, so inverting any logarithm value y always returns base to the power of y.

When the antilog result needs to be expressed in the same exponent form used in log tables, the exponential notation calculator converts the decimal answer into a mantissa times a power of the base for the same number.