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Euler Totient Function Calculator

Work out euler totient function instantly with clear inputs, formula shown and shareable results.

About Euler Totient Function Calculator

Euler's totient φ(n) counts the integers from 1 to n coprime to n. It is computed as n·Π(1 − 1/p) over the distinct prime factors, and equals n − 1 exactly when n is prime.

Formula

Euler's totient

φ(n) = n · Π over distinct primes p | n of (1 − 1/p)

Worked example

With the default values below, Euler Totient Function Calculator returns φ(n) of 12. Change any input above and every figure here is recalculated in your browser.

Inputs used

Numberminimum 1
36
Compare withminimum 1
37

Results

φ(n)
12
Fraction of numbers below n that are coprime to it
0.33333333
Prime factorisation
2^2 × 3^2
φ of the comparison number
36

Step by step

  1. 1Values used
  2. 2Euler's totient
  3. 3φ(n)= 12
  4. 4Fraction of numbers below n that are coprime to it= 0.33333333
  5. 5Prime factorisation= 2^2 × 3^2
  6. 6φ of the comparison number= 36

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is φ(36)?

36 = 2² × 3², so φ = 36 × ½ × ⅔ = 12.

Why does it matter for RSA?

RSA encryption relies on Euler's theorem a^φ(n) ≡ 1 (mod n) to construct the decryption exponent.

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