Antilog Calculator: Inverse Log with Steps & Table

Creator: Parker RowlandReviewer: Yulduz Zaripova

The antilog of a number is the base raised to that number. Antilog of 2 in base 10 is 100, because 10² = 100. Antilog of 1.5 is about 31.62, and antilog of -1 is 0.1. Enter your log value and base in the calculator above, or use the reference table below to find any antilog value instantly. This page covers the antilog formula, base 10 and base e (natural) antilogs, worked examples with the exact numbers people search, and a full lookup table.

What is an antilog?

An antilog is the reverse of a logarithm. A logarithm asks "what power gives this number?" An antilog does the opposite: it takes the power and gives you back the original number.

Put simply, if the log of a number is y, then the antilog of y returns that number. The word "antilog" is short for antilogarithm, and it means the same thing as inverse log.

Here is the idea in one line. If log₁₀(1000) = 3, then antilog₁₀(3) = 1000. The log turned 1000 into 3. The antilog turns 3 back into 1000.

You raise the base to the log value. Base 10 raises 10 to the power. Base e raises e (about 2.718) to the power. That single step is the whole operation.

What is the antilog formula?

The antilog formula is the base raised to the log value. It changes with the base you use.

Base 10 (common antilog):

antilog(x) = 10^x

If log₁₀(y) = x, then y = 10^x.

Base e (natural antilog):

antilog(x) = e^x

Here e is about 2.718. This is the inverse of the natural log (ln).

Any base b:

antilog(x) = b^x

If log_b(y) = x, then y = b^x.

So to take an antilog, you only need two things: the log value and the base. Raise the base to that value and you have your answer.

Antilog table (base 10 and base e values)

This table gives the antilog for common log values in both base 10 and base e. Find your log value in the first column and read across.

For values between the rows, use the calculator at the top of the page. It handles any decimal, negative, or large log value in base 10, base e, base 2, or any base you enter.

Antilog worked examples

Here are the antilog values people look up most often, solved step by step. Base 10 is assumed unless natural log is stated.

Antilog of 1.5

antilog₁₀(1.5) = 10^1.5 = 31.6228

10^1.5 is the same as 10¹ × 10^0.5 = 10 × 3.1623 = 31.62. In base e, antilog(1.5) = e^1.5 = 4.4817.

Antilog of -1

antilog₁₀(-1) = 10^-1 = 0.1

A negative log value gives a result less than 1. Here 10^-1 is 1 divided by 10, which is 0.1. In base e, antilog(-1) = e^-1 = 0.3679.

Antilog of 2

antilog₁₀(2) = 10² = 100

This is the classic example. The log of 100 is 2, so the antilog of 2 is 100. In base e, antilog(2) = e² = 7.3891.

Antilog of 2.303

antilog₁₀(2.303) = 10^2.303 = 200.91

This value shows up often because ln(10) is about 2.303. In base e, antilog(2.303) = e^2.303 = 10.004, which is close to 10. That is exactly why 2.303 links natural log and base 10 log.

Antilog of -3

antilog₁₀(-3) = 10^-3 = 0.001

Each negative whole number moves the decimal one place left. 10^-3 is 1 divided by 1000, which is 0.001.

Antilog of 0.301

antilog₁₀(0.301) = 10^0.301 = 1.9999

The log of 2 is about 0.301, so the antilog of 0.301 returns very close to 2. This is a common check when reading a log table.

How do you calculate antilog by hand?

You calculate an antilog by raising the base to the log value. Follow these steps.

• Step 1. Write down the log value and note the base. Base 10 is the default for common logs. Base e is used for natural logs.
• Step 2. Set up the power. For base 10 write 10^x. For base e write e^x.
• Step 3. Split the exponent if it helps. For antilog(2.5), write 10² × 10^0.5 = 100 × 3.1623 = 316.23.
• Step 4. Round only at the end. Rounding in the middle throws off the final answer, especially with decimals.

For a quick check, take the log of your answer. If you get back the value you started with, the antilog is correct.

How do you do antilog on a calculator?

Most scientific calculators do not have a button labelled "antilog." You use the power function instead, because antilog is just the base raised to a power.

• For base 10 antilog: press the 10^x key, then enter your value. On many calculators this is the second function above the "log" button, so you press SHIFT or 2nd, then log. Example: for antilog of 1.5, press 10^x then type 1.5 to get 31.62.
• For natural antilog (base e): use the e^x key, usually the second function above the "ln" button. Press SHIFT or 2nd, then ln, then enter your value.
• On a phone calculator: turn the phone sideways for scientific mode, then use the 10^x or e^x key the same way.

If you would rather skip the button hunting, the calculator at the top of this page does it in one click for any base.

Antilog vs logarithm: what is the difference?

A logarithm and an antilog are opposite operations. One compresses a number into a power, the other expands the power back into the number.

A logarithm answers: what power do I raise the base to, to get this number? An antilog answers: what number do I get if I raise the base to this power?

They cancel each other out. Take the log of a number, then the antilog of that result, and you are back where you started.

Is antilog the same as an exponential?

Yes, antilog and exponential are the same operation. Both raise a base to a power. When you take the antilog of x in base 10, you are computing the exponential 10^x. When you take the natural antilog, you are computing e^x, which is the exponential function.

The names differ by context. "Antilog" is used when you are reversing a specific log value, often from a log table or after solving a log equation. "Exponential" is used when you are describing the function or growth in general. The math underneath is identical.

What is inverse log and how is it different from antilog?

Inverse log and antilog mean the same thing. Both undo a logarithm and return the original number. Search terms like "inverse log calculator" and "antilog calculator" are asking for the exact same operation.

Inverse log base 10 is 10^x. Inverse natural log (the inverse of ln) is e^x. So an inverse ln calculator and a natural antilog calculator do the same job. Whichever term your textbook uses, the calculation is the base raised to your value.

Where is antilog used?

Antilog shows up any time a value was stored on a log scale and you need the real number back.

• Chemistry (pH): pH is the negative log of hydrogen ion concentration. To go from pH back to concentration, you take an antilog. For pH 4, the concentration is 10^-4 mol/L.
• Sound and signals (decibels): decibels use a log scale. Converting a decibel reading back to a power ratio needs an antilog.
• Earthquakes (Richter scale): magnitude is logarithmic. Antilog converts magnitude into relative energy or amplitude.
• Statistics: data is often log transformed to reduce skew. After analysis, antilog puts results back on the original scale.
• Finance and growth: exponential growth models run through logs. Antilog converts a growth exponent back into an actual value.

Common antilog mistakes to avoid

• Using the wrong base. Base 10 antilog is 10^x, natural antilog is e^x. Check which log your problem uses before you start. Mixing them gives very different answers.
• Confusing log with antilog. If the question gives you a number and asks for the power, that is a log. If it gives you a power and asks for the number, that is an antilog.
• Rounding too early. Round only the final result. Rounding a decimal exponent partway through changes the answer a lot.
• Forgetting the antilog step. After solving a log equation, you still have a log value. Apply the antilog to get the actual number.

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