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Antilog Calculator | Get antilog for base 10, e or custom

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Find the antilog of any logarithm — base 10, natural or custom — returning the original number with the exponent form shown. Useful for reversing log-scale work in pH, decibels, chemistry and exponential growth problems.

Last updated: June 2026 · Free · No sign-up required

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Results

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Quick reference

antilog (10^x)Result
10^01
10^110
10^2100
10^2.3010≈ 200
10^-10.1

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Interpretation guide

Baseantilog of x
10 (common)10^x
e (natural)e^x = exp(x)
2 (binary)2^x
any bb^x

lightbulb Worked example: pH 3.4 back to ion concentration

Orange juice has a pH of 3.4. What is its hydrogen-ion concentration? pH is a negative base-10 logarithm, so [H⁺] = 10^(−pH) = 10^−3.4. Split the exponent: 10^−3.4 = 10^0.6 × 10^−4 ≈ 3.981 × 10^−4 mol/L.

Result: ≈ 3.98 × 10⁻⁴ mol/L (≈ 0.000398 mol/L).

What this means: Each whole pH unit is a factor of ten: at pH 2.4 the concentration would be ten times higher (≈ 0.00398 mol/L). The antilog simply expands the compressed logarithmic scale back into the real concentration — the same undoing works for decibels and Richter magnitudes.

Formula & methodology

Formula: antilog_b(x) = b^x; common antilog = 10^x; natural antilog = e^x

How antilog is computed

The antilogarithm reverses a logarithm: if log_b(y) = x, then y = bˣ.

antilog_b(x) = bˣ — common antilog = 10ˣ, natural antilog = eˣ

  • Pick the base: 10 for decibels, pH, and Richter scales; e ≈ 2.71828 for continuous growth; or any custom base.
  • Raise the base to your number: antilog₅₀(2.3010) = 10^2.3010 ≈ 200.
  • Fractional and negative inputs are fine: antilog₅₀(−3.4) ≈ 3.98 × 10⁻⁴.

Reading the result

Antilogs undo compressed log scales. A pH of 3.4 means [H⁺] = 10^−3.4 ≈ 0.000398 mol/L, and a 20 dB gap means antilog₅₀(2) = 100 times the power. The base must be positive and not equal to 1.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is an antilog?
The antilog (antilogarithm) is the inverse of a logarithm. If log_b(y) = x, then the antilog of x in base b is y = b^x. In other words, taking the antilog undoes the log: it raises the base to the power of your value. The common antilog uses base 10, so antilog(x) = 10^x.
How do you calculate antilog?
Raise the base to the power of the number. For the common (base-10) antilog of 3, compute 10^3 = 1,000. For the natural antilog of 1, compute e^1 = 2.718. On a calculator, the antilog button is usually 10^x (the shift of the log key) or e^x (shift of ln).
What is the difference between common and natural antilog?
The common antilog uses base 10: antilog(x) = 10^x, and it inverts log10. The natural antilog uses base e ≈ 2.71828: antilog(x) = e^x = exp(x), and it inverts ln. Use whichever base matches the logarithm you are reversing; mixing them gives wrong results.
What is the antilog of 2?
The antilog is the inverse of the logarithm: for base 10, antilog of 2 means 10² = 100. For the natural base e, antilog of 2 is e² ≈ 7.389. In general, antilog_b(x) = b^x. Choose the same base as the logarithm you started with, and the calculator returns the original number, which is useful in pH, decibel, and exponential-growth work.
Where are antilogs used?
Antilogs convert logarithmic scales back to linear values. They appear in decibels (sound), pH (chemistry), the Richter scale (earthquakes), and anywhere data is stored or computed in log form and then needs to be read as an ordinary number. Before electronic calculators, antilog tables were used alongside log tables for multiplication.
How do you convert pH back to hydrogen ion concentration?
pH is a negative base-10 log, so undo it with the common antilog: [H⁺] = 10^(−pH). For pH 3.4, [H⁺] = 10^−3.4 ≈ 3.98 × 10⁻⁴ mol/L — about 0.4 millimoles per liter, roughly the acidity of orange juice. Each whole pH unit changes the concentration tenfold.
What is the natural antilog of 1?
e^1 = e ≈ 2.71828. The natural antilog is just the exponential function: antilog_e(x) = e^x. It inverts the natural logarithm, so ln(2.71828) = 1 and antilog_e(1) = 2.71828. Continuous-growth formulas in finance and biology use this form.
How do antilogs undo logarithmic scales?
Every log scale compresses ratios into differences, and the antilog expands them back. A sound at 60 dB versus 40 dB differs by 20 dB, and antilog₅₀(20/10) = 100 — the louder sound carries 100 times the power. Decibels, Richter magnitudes, and pH all work this way.
Can antilog handle fractional or negative inputs?
Yes — any real number works. antilog₅₀(2.5) = 10^2.5 ≈ 316.23, and antilog₅₀(−2) = 0.01. Fractional inputs give roots of the base (10^0.5 = √10 ≈ 3.162), while negative inputs give fractions. Only the base must stay positive and not equal 1.

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