Antilog Calculator
Calculate the inverse logarithm — antilog_b(y) = b^y — in any base. Enter the log value, select base 10, e, 2, or custom, and get the original number instantly with verification.
You might also need
How It Works
Enter the log value y and keep base 10 selected. The result is 10^y. The verify line shows log₁₀(result) = y to confirm. For pH: enter the negative pH value (e.g. −3 for pH 3) → [H⁺] = 10^(−3) = 0.001 mol/L. For decibels: intensity = 10^(dB/10) × reference intensity.
antilog₁₀(y) = 10^y | antilog₁₀(−pH) = [H⁺]antilog₁₀(3) = 1000 | antilog₁₀(−3) = 0.001 | antilog₁₀(1.5) = 31.62Select base e. antilogₑ(y) = eʸ — the same as the exponential function. Used to reverse ln in calculus solutions. If you solved ln(x) = 2.5 for x: enter 2.5, base e → result e^2.5 ≈ 12.182. The verify line confirms: ln(12.182) ≈ 2.5.
antilogₑ(y) = eʸ | e^ln(x) = x | e⁰ = 1 | e¹ ≈ 2.718antilogₑ(2) = 7.389 | antilogₑ(0.5) = 1.649 | antilogₑ(−1) = 0.368Select base 2. antilog₂(y) = 2^y. If log₂(N) = 10 (10 bits of information), then N = 2^10 = 1024. Byte sizes: 2^8 = 256, 2^16 = 65536, 2^32 ≈ 4.3 billion. Network subnets: /24 gives 2^8 = 256 addresses, /16 gives 2^16 = 65536.
antilog₂(y) = 2^y | 2^10 = 1024 | 2^20 = 1048576antilog₂(8) = 256 | antilog₂(10) = 1024 | antilog₂(16) = 65536Type any base in the custom base field — must be positive and not equal to 1. antilog₅(3) = 5³ = 125. antilog₃(4) = 3⁴ = 81. Useful when working with a specific log base imposed by a formula or dataset. The verify line always confirms by computing log_b(result) = y.
antilog_b(y) = b^y where b > 0, b ≠ 1antilog₅(3) = 125 | antilog₃(4) = 81 | antilog₁₆(2) = 256Fractional antilog: antilog₁₀(0.5) = 10^0.5 = √10 ≈ 3.162. General rule: antilog_b(1/n) = ⁿ√b. Negative antilog: antilog₁₀(−n) = 1/10^n — always a positive number less than 1. There is no undefined output — antilog is defined for all real y values.
antilog_b(1/n) = ⁿ√b | antilog_b(−n) = 1/b^nantilog₁₀(0.5) = √10 ≈ 3.162 | antilog₁₀(−2) = 0.01Quick Reference
Common antilog values — verify these in the calculator above.
Base 10
antilog₁₀(1)
10
Base 10
antilog₁₀(2)
100
Base 10
antilog₁₀(3)
1000
Base 10 (pH)
antilog₁₀(−3)
0.001
Base e (eˣ)
antilogₑ(1)
2.71828
Base e (eˣ)
antilogₑ(2)
7.38906
Base 2 (binary)
antilog₂(8)
256
Fractional
antilog₁₀(0.5)
3.16228
Tips & Shortcuts
For pH problems, enter the pH as a negative number directly: pH 4 → enter −4, base 10 → result 0.0001 mol/L. No need to negate manually.
The verify line (log_b(result) = y) is your built-in accuracy check. If it shows your original y value, the antilog is correct.
Fractional y values give roots: antilog₁₀(0.5) = √10, antilog₁₀(1/3) = ∛10. The Exponent tab with fractional exponents gives the same result.
antilog₁₀(y) grows extremely fast. antilog₁₀(10) = 10 billion, antilog₁₀(100) = 10^100 (a googol). For very large y the result displays in scientific notation automatically.
Switch to the Log/Ln tab to reverse: if antilog₁₀(y) = 1000, then log₁₀(1000) = 3. The two tabs are mathematical inverses of each other.
Common Mistakes
Confusing antilog₁₀(y) with 10 × y
antilog₁₀(3) = 10³ = 1000, not 10 × 3 = 30. Antilog is exponentiation, not multiplication. The base is raised to the power of y.
Entering a positive y for pH when you need [H⁺]
pH = −log₁₀[H⁺], so [H⁺] = 10^(−pH). For pH 5, enter −5 (negative), not 5. antilog₁₀(5) = 100000, antilog₁₀(−5) = 0.00001 — a difference of 10 billion.
Using antilog when the original operation was ln, not log₁₀
Always match the base. If the original log used base e (ln), use antilog with base e. antilogₑ(3) ≈ 20.09, but antilog₁₀(3) = 1000 — completely different results from the same input.
Expecting antilog of 0 to be 0
antilog_b(0) = b⁰ = 1 for any base b. Zero exponent always equals 1. If you get 1 when expecting 0, check that you entered the right value — 0 is not a valid log result for an original value of 0 (log(0) is undefined).
Using the Exponent tab instead of Antilog for pH and chemistry
Both give the same result, but the Antilog tab is purpose-built: it accepts the log value directly and shows the verify confirmation. The Exponent tab requires you to enter the base (10) and the exponent (−pH) separately — more steps for the same answer.
Frequently Asked Questions
Antilog (inverse logarithm) reverses a logarithm. The formula is antilog_b(y) = b^y. If you computed log_b(x) = y and now want x back, antilog_b(y) gives you x. Example: log₁₀(1000) = 3, so antilog₁₀(3) = 10³ = 1000 — the original number is recovered exactly.
antilog₁₀(3) = 10³ = 1000. The pattern: antilog₁₀(0) = 1, antilog₁₀(1) = 10, antilog₁₀(2) = 100, antilog₁₀(3) = 1000. Each whole-number step multiplies the result by 10. For decimals: antilog₁₀(1.5) = 10^1.5 ≈ 31.623.
They compute the same result — b^y — but from different starting points. Antilog is framed as reversing a logarithm: you have a log value and want the original number. The Exponent tab (aⁿ) is framed as raising a base to a power. Both give the same answer. Use antilog when recovering from a log operation; use Exponent when computing powers directly.
Antilog of a negative value is a positive fraction between 0 and 1. antilog₁₀(−1) = 10^(−1) = 0.1. antilog₁₀(−2) = 0.01. antilog₁₀(−6) = 0.000001. Negative log values represent numbers less than 1 in that base. This is essential in chemistry: [H⁺] = 10^(−pH), so pH 7 means [H⁺] = 10^(−7) = 0.0000001 mol/L.
Select base e in the Antilog tab. antilogₑ(y) = eʸ — identical to the exponential function eˣ. antilogₑ(0) = 1, antilogₑ(1) = 2.71828, antilogₑ(2) = 7.389, antilogₑ(−1) = 0.368. This reverses ln(x). Since ln and eˣ are perfect inverses: e^ln(5) = 5 exactly.
pH = −log₁₀[H⁺], so [H⁺] = 10^(−pH) = antilog₁₀(−pH). For pH 3: enter −3 and base 10 → result 0.001 mol/L. For pH 7: enter −7 → result 0.0000001 mol/L. This also works for pOH, pKa, and pKb — all use base-10 antilog to recover concentrations from their negative log forms.
antilog₂(y) = 2^y — it reverses log₂ operations. If a compression algorithm reports log₂(N) = 8 bits, then N = 2^8 = 256 distinct values. In information theory: 3 bits of entropy → 2³ = 8 equally likely outcomes. In networking: a /24 subnet has 2^(32−24) = 2^8 = 256 addresses. Enter the bit count and base 2 to get the count instantly.
Related Calculators
Voltage Divider Calculator
Calculate output voltage of a resistor voltage divider.
Resistor Calculator
Decode resistor color bands and calculate resistance.
Basic Calculator
Fast arithmetic: add, subtract, multiply, divide.
Random Number Generator
Generate random integers within any range.
Number Sequence Calculator
Find the nth term of arithmetic or geometric sequences.
Big Number Calculator
Perform arithmetic on numbers with hundreds of digits.