Inverse Log Calculator
The inverse log, also called the antilog, reverses a logarithm: if logb(x) = y, then x = by. Enter a log value and its base and this calculator returns the original number, with the substitution step and a scientific-notation readout for very large or very small answers.
Antilog
The base must be a positive number other than 1. Leave the base blank to use 10.
Quick Answer
The antilog of 2 in base 10 is 100: the calculator raises the base to the log value, 102 = 100, and also shows the scientific notation 1.000000e+2 and the one-line step. The calculator above is pre-filled with this exact example, and the base can be 10, e, 2, or any positive number other than 1.
Key takeaways
- An antilog is just a power: antilogb(y) = by. The base of the antilog must match the base of the original logarithm.
- A blank base means base 10 here, the same convention textbooks and handheld calculators use for a log written with no base.
- The sign of the log value decides the size of the answer: positive gives a result above 1, zero gives exactly 1, negative gives a fraction between 0 and 1.
- The Steps line keeps the full computed value even when the headline answer switches to scientific notation.
- Quick Answer
- How to use the inverse log calculator
- The inverse log formula, and why the base has rules
- Worked examples across the three named bases
- Where antilogs do real work: pH, decibels, earthquakes
- Why the headline answer sometimes switches to scientific notation
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the inverse log calculator
Enter the log value, set the base, and click Calculate. Results stay hidden until you click.
- Logarithm value (y): type the logarithm you want to undo. It can be a whole number, a decimal such as 0.301, zero, or a negative number such as -2.
- Base (b): type the base of the original logarithm, tap a quick-base button for 10, e, or 2, or leave the field blank for base 10. Any positive base other than 1 works, including fractions such as 0.5.
- Read the three outputs: the antilog itself, the same answer in scientific notation, and the Steps line showing the substitution, for example 10^0.301 = 1.9998618696327441.
- Copy or share: the buttons inside the result copy one line with all three outputs, handy for homework or a lab notebook.
If you are working in the other direction, from a number to its logarithm or its power form, the exponential and logarithmic equations calculator solves the full equation rather than this single step.
The inverse log formula, and why the base has rules
The formula is x = by: if y = logb(x), raising b to the power y returns x exactly. The NIST Digital Library of Mathematical Functions, in its definitions for the logarithm and exponential functions, treats the two as inverse operations on the same base, which is why the base here must be positive and not 1.
y = logb(x). You know y and b; x is hidden.
Compute by. This is the entire antilog step.
x = by. Check: logb(x) gives y back.
Base 1 is banned because every power of 1 is 1, so log1 cannot distinguish numbers and has no inverse. Zero and negative bases break the real-valued logarithm the same way, so the calculator rejects them with a message instead of printing a misleading number. Bases between 0 and 1 are valid and behave in reverse: 0.52 = 0.25, so a larger log value gives a smaller answer. The two named cases are the common log, x = 10y, and the natural log, x = ey, where e is about 2.718281828459045. One quirk worth knowing: the quick-base e button writes the full value of e into the base field, and only that exact value takes the dedicated ey path in the code; typing a rounded 2.71828 computes 2.71828y instead, which differs only far into the decimal places.
For the power itself, an exponent calculator handles general base-and-exponent work, while this page is built for the log-reversal framing: the input is a logarithm, not an arbitrary exponent.
Worked examples across the three named bases
Every row below is a verified run of the calculator above, including the exact Steps text it prints.
| Log value (y) | Base (b) | Antilog | Scientific notation | Steps line |
|---|---|---|---|---|
| 2 | 10 | 100 | 1.000000e+2 | 10^2 = 100 |
| 1 | e (quick button) | 2.7182818285 | 2.718282e+0 | e^1 = 2.718281828459045 |
| 10 | 2 | 1024 | 1.024000e+3 | 2^10 = 1024 |
| 0.301 | 10 | 1.9998618696 | 1.999862e+0 | 10^0.301 = 1.9998618696327441 |
| -2 | 10 | 0.01 | 1.000000e-2 | 10^-2 = 0.01 |
| 3 | 5 | 125 | 1.250000e+2 | 5^3 = 125 |
The 0.301 row is the classic log-table check: log10(2) is about 0.301, so the antilog of 0.301 should land near 2, and it does, at 1.9998618696. It is not exactly 2 because 0.301 is itself a rounded logarithm. Older versions of this page quoted that answer as 1.9999, a rounding the tool never actually prints; the table above uses the tool’s real output. Rewriting a power in the other direction, as exponential form, is covered by the convert to exponential form calculator.
Where antilogs do real work: pH, decibels, earthquakes
Antilogs earn their keep wherever a scale is logarithmic and you need the physical quantity back. Three standard cases, each one a single run of the tool above:
Chemistry: pH 7
1.000000e-7 mol/L
Hydrogen-ion concentration is 10-pH. Enter y = -7, base 10. The OpenStax Chemistry treatment of pH and pOH defines the scale this way.
Acoustics: 30 dB
1,000x power
A power ratio in decibels is 10 x log10(ratio), so the ratio is 10dB/10. Enter y = 3, base 10, and the tool returns 1000.
Seismology: magnitude 6
1.000000e+6 amplitude
Each whole magnitude step is a 10x amplitude step. Enter y = 6, base 10: the headline itself switches to scientific notation. The USGS guide to magnitude, energy release, and shaking intensity explains the scale.
Growth problems run the same way with base e: a continuous-growth exponent from a model, entered as the log value with the e quick button, returns the growth factor. For the growth rate side of that work, the exponential growth calculator builds the full time path instead of a single reversal.
Why the headline answer sometimes switches to scientific notation
The headline switches format at two fixed points, and knowing them stops the output looking like a bug. Below 0.0001 and at 1,000,000 or above, the antilog prints in scientific notation with six digits after the decimal point, so 10-5 shows as 1.000000e-5 and 106 as 1.000000e+6.
Between those points the headline trims the computed value to 10 decimal places, which is why 100.5 shows as 3.1622776602 while the Steps line carries the full 3.1622776601683795. Exactly 0.0001 stays in plain form (10-4 shows as 0.0001), because the switch is strictly below that value. Two extreme cases are worth knowing before they surprise you: 10400 overflows and the tool honestly prints Infinity in all three outputs, and 10-400 underflows to 0 in the Steps line, shown as 0.000000e+0 in the headline. Neither is a usable physical answer; both are the true limits of double-precision arithmetic.
What competing calculators miss
The antilog itself is one line of math, so rival pages differ on base freedom, working shown, and how honestly they document edge behaviour:
- CalculatorLib’s inverse log calculator restricts the base to a fixed list of three (10, e, 2). A problem in base 5, such as log5(x) = 3, cannot be entered at all. This tool takes any positive base other than 1, typed directly.
- Helping With Math’s antilog calculator frames the antilog as 10x in its formula section, as if base 10 were the only case, and its result panel has shown placeholder values (Value: 2, Antilog: 2) that were never computed. Base e and custom bases need the general by form used here.
- OmexCalculator’s antilog page tells users to leave the base empty for a natural (base e) antilog, which clashes with the textbook convention, followed here and by most rivals, that a blank or unwritten base means 10. Guessing wrong on that point silently changes every answer by a large factor.
- Omni Calculator’s antilog calculator has the strongest explainer of the group, but the tool is a general any-base form with no substitution trace for your numbers and no statement of when its display switches notation. The Steps line here shows your exact substitution, and the notation thresholds are documented on this page.
- MiniWebTool’s antilog calculator adds a base-comparison table and a curve chart, genuinely useful extras. What it does not document is the display behaviour at the extremes, the overflow and underflow cases this page states openly.
Frequently asked questions
The inverse log, or antilog, undoes a logarithm. If y = log base b of x, the antilog is b raised to the power y, which returns the original number x.
Every power of 1 is 1, so a logarithm to base 1 is undefined and has no inverse. The calculator also rejects zero and negative bases for the same reason: real logarithms are only defined for positive bases other than 1.
The calculator uses base 10, the common logarithm. That matches the convention in most textbooks and on most handheld calculators, where a log written with no base means base 10.
Yes. A negative log value gives a result between 0 and 1 (10 to the power -2 is 0.01), and decimals are handled at full precision: 10 to the power 0.5 shows as 3.1622776602.
On most scientific calculators, press SHIFT then the LOG key to get 10 to the power x, or SHIFT then LN for e to the power x. Enter the log value first, then the function, then equals.
There is none. Antilog is the traditional name, inverse log is the descriptive name, and both mean the base raised to the log value: b to the power y.
The headline result switches to scientific notation with six digits after the decimal point when the answer is below 0.0001 or reaches 1,000,000, because long strings of zeros are easy to misread. The Steps line always shows the full computed value, and extreme inputs such as 10 to the power 400 overflow to Infinity.
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References
- National Institute of Standards and Technology, Digital Library of Mathematical Functions. DLMF Section 4.2: Definitions of the Logarithm and Exponential Functions. Accessed October 22, 2026.
- OpenStax, Rice University. Algebra and Trigonometry 2e, Section 6.3: Logarithmic Functions. Accessed October 22, 2026.
- OpenStax, Rice University. Algebra and Trigonometry 2e, Section 6.1: Exponential Functions. Accessed October 22, 2026.
- OpenStax, Rice University. Chemistry 2e, Section 14.2: pH and pOH. Accessed October 22, 2026.
- U.S. Geological Survey, Earthquake Hazards Program. Earthquake Magnitude, Energy Release, and Shaking Intensity. Accessed October 22, 2026.
- Paul Dawkins, Lamar University. Paul’s Online Math Notes, Algebra: Logarithm Functions. Accessed October 22, 2026.