Antilog Calculator
Calculate antilogarithm (inverse log) for any base. Find the value of b^x where b is the base.
Antilog Input
Formula
antilog10.00(2) = 10.002
Antilog (Base 10.00)
1.000000e+2
= 100
Common Antilog Values
| x | 10^x | e^x |
|---|---|---|
| -2 | 0.01 | 0.1353 |
| -1 | 0.1 | 0.3679 |
| 0 | 1 | 1.0000 |
| 1 | 10 | 2.7183 |
| 2 | 100 | 7.3891 |
| 3 | 1000 | 20.0855 |
Understanding Antilogarithm
Definition
The antilogarithm is the inverse operation of the logarithm. If logb(y) = x, then antilogb(x) = y = bx
Common Types
- Common antilog: 10x (inverse of log10)
- Natural antilog: ex (inverse of ln)
- Binary antilog: 2x (inverse of log2)
What Is an Antilog Calculator?
An antilog calculator computes the inverse of a logarithm — it answers the question: "What number y satisfies logb(y) = x?" Mathematically, the antilog of x in base b is simply bx. This calculator handles common antilogs (10x), natural antilogs (ex), binary antilogs (2x), and any custom base you choose.
Antilogarithms are essential in fields where data is logged for compression or analysis and then needs to be converted back to its original scale. In chemistry, pH values are logarithms of hydrogen ion concentration — the antilog converts a pH of 3 back to [H⁺] = 10⁻³. In seismology, the Richter scale magnitude is logarithmic, and the antilog gives the actual energy released. In audio engineering, decibel levels are logarithmic relative to a reference, and the antilog recovers the physical intensity.
The calculator also provides a quick-lookup table of common antilog values for x from −2 to 3, making it easy to verify manual calculations or to get a rough sense of scale without recalculating each time.
The Antilog Formula
The antilogarithm is defined as the base raised to the power of the given logarithm value. If you know logb(y) = x, then y = bx.
Antilog Formula
Where:
- b= The logarithm base — 10 for common logs, e (~2.718) for natural logs, 2 for binary logs, or any positive number
- x= The logarithm value (the input). Can be any real number — negative values produce fractional results
Understanding the Results
The calculator computes antilogs for four bases simultaneously so you can compare across different logarithmic scales:
| Antilog Type | Formula | Use Case |
|---|---|---|
| Custom Base | bx | General-purpose — enter any base you need |
| Common (10ˣ) | 10x | Chemistry (pH), sound (dB SPL), earthquake magnitude |
| Natural (eˣ) | ex | Continuous growth/decay, population models, calculus |
| Binary (2ˣ) | 2x | Computer science, information theory, data size estimates |
Results are displayed in exponential notation for readability when values are very large or very small. A quick-reference table below the inputs shows antilog values at integer x for the most common bases.
How to Use This Calculator
Operating the antilog calculator takes just two inputs:
- Enter the logarithm value (x): This is the exponent — the result of a previous log calculation that you want to reverse. Enter any real number; negative values produce fractional antilogs (for example, 10−2 = 0.01).
- Choose the base (b): Type any positive number. Use the quick-select buttons for the three most common bases: 2 (binary), e (natural, ≈ 2.718), and 10 (common).
- Read the results: The highlighted result card shows the custom-base antilog in both exponential and decimal notation. Below it, three additional cards display the common, natural, and binary antilogs for the same x value so you can instantly see the comparison.
Real-World Applications
Antilogs are used whenever data has been log-transformed and needs to be interpreted on its original scale. In chemistry and biology, the pH of a solution is pH = −log10[H⁺], so the hydrogen ion concentration is recovered by [H⁺] = 10−pH. A pH of 7 means [H⁺] = 10−7 M, and an acidic pH of 3 gives [H⁺] = 10−3 M — a ten-thousand-fold difference.
In finance, logarithmic returns are used for modeling asset prices because they are additive over time whereas simple returns are multiplicative. To convert a log return of 0.05 back to a price ratio, you compute e0.05 ≈ 1.0513, meaning the asset grew by about 5.13%. In seismology, a magnitude-5 earthquake releases 105 times the energy of a reference quake, while a magnitude-7 quake releases 107 — a 100-fold increase for just two magnitude points.
Worked Examples
Finding a Common Antilog
Problem:
If log₁₀(y) = 2, what is y?
Solution Steps:
- 1Enter x = 2 and set base = 10.
- 2Apply the formula: y = 10² = 10 × 10.
- 3Compute: 10² = 100.
Result:
y = 100. The common antilog of 2 is 100 — meaning 10² = 100.
Converting a pH Value to Concentration
Problem:
A solution has pH = 4.5. Find the hydrogen ion concentration.
Solution Steps:
- 1pH = −log₁₀[H⁺], so [H⁺] = 10⁻⁴·⁵.
- 2Enter x = −4.5 and base = 10 in the calculator.
- 3Compute: 10⁻⁴·⁵ ≈ 3.1623 × 10⁻⁵ M.
Result:
[H⁺] ≈ 3.162 × 10⁻⁵ moles per liter, displayed in exponential notation.
Natural Antilog of a Log Return
Problem:
A stock's log return over one month is 0.03. What is the price multiplier?
Solution Steps:
- 1Enter x = 0.03 and select the natural base (e) using the quick-select button.
- 2Apply the formula: e⁰·⁰³ using Math.exp(0.03).
- 3Compute: e⁰·⁰³ ≈ 1.0305.
Result:
The price multiplier is approximately 1.0305, meaning roughly a 3.05% increase.
Tips & Best Practices
- ✓Remember: log and antilog are inverses. If log₁₀(1000) = 3, then antilog₁₀(3) = 1000.
- ✓Use the quick-select base buttons (2, e, 10) to avoid typing common values repeatedly — they use the exact value of e from Math.E.
- ✓The decimal display below the exponential notation makes it easy to read values in familiar format — no mental conversion needed.
- ✓For very large antilogs, the exponential notation (e.g., 1.2345e+20) is the clearest way to read the result.
- ✓Negative x inputs produce fractional results — antilog₁₀(−1) = 0.1, antilog₁₀(−2) = 0.01, and so on.
- ✓The quick-reference table at the bottom shows integer x values from −2 to 3 for both 10ˣ and eˣ — useful for spot-checking.
Frequently Asked Questions
Sources & References
Last updated: 2026-06-06
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun