The Antilog Calculator computes the antilogarithm (inverse logarithm) of any value in base 10, natural base e, or base 2. Reverses the logarithm: antilog_b(x) = b^x. Essential in chemistry (pH to concentration), acoustics (dB to power ratio), and seismology (Richter to energy).
100
2
2
4.60517019
100
2
2
4.60517019
Logarithms compress huge numerical ranges into manageable scales — pH, decibels, Richter magnitude, and musical octaves all use logarithmic scales. But when you need to work backwards from a logarithmic value to the underlying quantity — convert a pH to hydrogen ion concentration, or a dB reading to power ratio — you need the antilog. The calculator for antilogarithm reverses any logarithm in any base instantly.
The antilogarithm is the inverse function of the logarithm. If log_b(x) = y, then antilog_b(y) = x:
antilog_b(y) = b^y
The three most common cases:
The logarithmic equation calculator handles the forward direction and equations involving logarithms. The change of base calculator converts between logarithm bases when needed.
In chemistry, the "p" prefix universally means −log₁₀. Antilog converts back to the underlying concentration:
The reverse pH problem — "what concentration of NaOH gives pH 12?" — requires antilog: [OH⁻] = 10^(−pOH) = 10^(−2) = 0.01 mol/L. Use this online calculator for any such conversion.
The decibel scale compresses the enormous range of audible sound pressures into a convenient 0–140 dB range. Converting back from dB to power ratio or pressure ratio requires antilog:
Power ratio = 10^(dB/10) — for power-based dB (sound power level, electrical power)
Pressure ratio = 10^(dB/20) — for amplitude-based dB (sound pressure level, voltage)
A 30 dB increase represents a power ratio of 10^(30/10) = 10^3 = 1,000× — three orders of magnitude. A sound at 85 dB SPL has a pressure 10^(85/20) = 10^4.25 = 17,783 times higher than the reference pressure of 20 μPa. The exponential growth calculator and logarithm and exponent calculators cover related exponential and logarithmic mathematics.
The Richter magnitude scale is logarithmic: each whole number increase represents a 10× increase in ground motion amplitude and approximately 31.6× increase in energy released (10^1.5 per magnitude unit). The energy E (in joules) for Richter magnitude M: log₁₀(E) ≈ 1.5M + 4.8, so E = 10^(1.5M + 4.8). A magnitude 7.0 earthquake: E = 10^(1.5×7 + 4.8) = 10^15.3 ≈ 2 × 10¹⁵ J — equivalent to about 475 kilotons of TNT. The antilog is the operation that converts these logarithmic scales back to physical quantities with meaningful units.
The antilogarithm reverses the logarithm operation. Given a base $$b$$ and an exponent $$x$$, the antilog is defined as:
$$\text{antilog}_b(x) = b^x$$
For common logarithms (base 10): $$\text{antilog}_{10}(x) = 10^x$$. For natural logarithms (base $$e$$): $$\text{antilog}_e(x) = e^x$$.
Verification: The result is verified by computing $$\log_b(b^x)$$, which must equal $$x$$. This uses the change of base formula: $$\log_b(y) = \frac{\ln(y)}{\ln(b)}$$.
The calculator also provides $$\log_{10}$$ and $$\ln$$ of the result for cross-reference with other logarithmic scales.
The Antilog Result is the value $$b^x$$. The Verification field confirms correctness by showing that $$\log_b(\text{result}) = x$$. Use the $$\log_{10}$$ and $$\ln$$ outputs when converting between logarithmic scales. For example, if you computed an antilog in base 10 and need the natural log equivalent, the $$\ln(\text{result})$$ field provides it directly.
Inputs
Results
antilog₁₀(3) = 10³ = 1000. Verification: log₁₀(1000) = 3 ✓
Inputs
Results
antilog_e(2) = e² ≈ 7.389. This is equivalent to exp(2). Verification: ln(7.389) ≈ 2 ✓
They are the same operation. The antilogarithm of $$x$$ in base $$b$$ is simply $$b^x$$. The term "antilog" emphasizes that it reverses a logarithm, while "exponentiation" describes the mathematical operation being performed.
Set the base to $$e \approx 2.71828$$ and enter your value as the exponent. The result is $$e^x$$, which is the inverse of $$\ln(x)$$.
In chemistry, pH = $$-\log_{10}[H^+]$$. To find the hydrogen ion concentration from pH, you compute the antilog: $$[H^+] = 10^{-\text{pH}}$$. For example, pH 4 gives $$[H^+] = 10^{-4} = 0.0001$$ M.
Yes. Any positive number can serve as a base. For example, $$0.5^3 = 0.125$$. The calculator accepts any base greater than zero.
Floating-point arithmetic introduces small rounding errors (typically around $$10^{-15}$$). This is a limitation of computer number representation, not a mathematical error.
A negative exponent gives a reciprocal: $$b^{-x} = \frac{1}{b^x}$$. For example, $$10^{-2} = 0.01$$. The calculator handles negative exponents correctly.
How helpful was this calculator?
5.0/5 (1 rating)
