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Antilog of a log value
The log value x and the base in — basex out, with the reversed log statement so you can verify the answer instantly. Base 10 is the everyday default; e and 2 cover science and computing.
CALCULATOR · MATH · LOGARITHMS
Antilog Calculator
The antilog of 2 at base 10 is 100 — because log10(100) = 2, so 100 is the number that logarithm came from. Enter any log value, pick base 10, e, or 2, and get the original number back — plus the reversed statement to check your work. Chemists use it to turn pH back into concentration; audio engineers use it to turn decibels back into ratios.
The 60-second rule
Antilog(x) = basex. A logarithm asks “10 to what power gives 100?” (answer: 2); the antilog runs the question backward: “102 is what?” (answer: 100). At the defaults: base 10, x = 2 → 102 = 100, and the check reads log10(100) = 2 — the reversed statement the calculator prints under every answer.
The worked example, line by line
Setup: log value x = 2, base 10.
The power. Antilog(2) = 102 = 10 × 10 = 100. The exponent becomes the multiplication.
The check. Reverse it: log10(100) = 2 — the logarithm of 100 really is 2, so the antilog is correct.
Branch — base e, x = 1: e1 = 2.71828 (Euler’s number, the base of natural logs). The check: ln(2.71828) = 1.
Branch — base 2, x = 10: 210 = 1024 — the kilobyte number, the most famous power of two in computing. The check: log2(1024) = 10.
Branch — base 10, x = −2: 10−2 = 1 ÷ 100 = 0.01. Negative exponents flip the answer into a fraction — this is exactly how pH math works. The check: log10(0.01) = −2.
Branch — base 10, x = 3: 103 = 1000. Each whole step of x multiplies the answer by the base — logarithms compress huge ranges into small numbers, and antilogs expand them back.
Output · formula · meaning
| Output | Formula | What it means |
|---|---|---|
| Antilog result | basex | 100 at the defaults — the original number the logarithm came from. |
| Reversed statement | logbase(result) = x | log10(100) = 2 at the defaults — run the answer backward to verify it. |
| Overflow flag | result exceeds ~1.8 × 10308 | “too large to display” — shown instead of a number when x is beyond about 308 at base 10. |
Who uses this
- The chemistry student: pH 3 means [H+] = 10−3 = 0.001 M — enters x = −3, base 10, and converts the log-scale pH back into a real concentration.
- The audio engineer: a 20 dB gain is 102 = 100× the amplitude — reverses decibels into the power ratio the faders actually apply.
- The student checking log homework: computed log10(1000) = 3 by hand, enters x = 3, and confirms the antilog comes back 1000 — the answer checks itself.
- The finance analyst: a log return of 0.693 at base e reverses to e0.693 = 2.0 — a doubling, converted from the log scale back into a plain growth factor.
Accuracy & limitations
Results are computed in IEEE-754 double precision — about 15–16 significant digits, exact for every classroom and engineering use. Overflow: inputs beyond about x = 308 at base 10 exceed the largest representable double (~1.8 × 10308), so the calculator shows “too large to display” instead of a wrong number. Results are shown rounded to 6 significant digits for readability (e1 displays as 2.71828, not the full 2.718281828459045). Base e uses your browser’s Math.E constant. The base is restricted to positive values other than 1 — a base of 1 has no meaningful logarithm (1x is always 1), so it is rejected.
Cite this calculatorBright Side Kit. “Antilog Calculator.” brightoolbox.com, 2026.
Bright Side Kit. "Antilog Calculator." https://brightoolbox.com/anti-log-calculator/ Accessed October 23, 2026.Frequently asked questions
What is an antilog?
The inverse of a logarithm: if log10(100) = 2, then the antilog of 2 (base 10) is 100. It recovers the original number a logarithm was taken from — computed as basex.
How do you find the antilog of 2?
Raise the base to the 2nd power: at base 10, 102 = 100. The check: log10(100) = 2. At base e the antilog of 2 is 7.38906; at base 2 it is 4.
What is the antilog of a negative number?
A number between 0 and 1: the antilog of −2 at base 10 is 10−2 = 0.01. Negative exponents move the decimal left — this is exactly how pH values convert into hydrogen-ion concentrations.
When do I use base e instead of base 10?
Use e (natural log) for science and growth math — pH-adjacent chemistry, continuous compounding, decay rates — and 10 (common log) for everyday scales like decibels, pH itself, and Richter magnitudes. Use 2 for computing and information theory.
What does “too large to display” mean?
Your x overflowed IEEE-754 double precision: beyond about x = 308 at base 10, the true answer exceeds ~1.8 × 10308, the largest number a browser can hold. The calculator refuses to print Infinity and says so honestly.
How is antilog used in chemistry?
pH is a negative log: pH = −log10([H+]). So a solution at pH 3 has [H+] = 10−3 = 0.001 moles per liter — enter x = −3, base 10, and the antilog does the conversion.
Is antilog the same as the log¹² button on my calculator?
Yes — log¹² (or 10x / ex) is the antilog key. It computes basex directly, which is exactly what this page does, with the base made explicit instead of hidden behind a shift key.