Euler's Totient Function (Phi φ(n)) Calculator
Local ProcessingCalculate Euler totient φ(n) counting integers up to n that are relatively prime to n.
How It Works & Processing Standards
Enter values above to calculate results automatically. Check each input field for guidance and units.
Tool processing runs in your browser. If you create a calculator or conversion share link, its values are included in the URL. See the privacy policy for account, analytics and advertising data.
φ(n) = n × Π(1 − 1/p) over the distinct prime factors p of n. For a prime p, φ(p) = p − 1.
How to Use Euler's Totient Function (Phi φ(n)) Calculator
- 1Enter nAn integer of 1 or more.
- 2Read the resultThe count of integers up to n that are coprime to n.
- 3Use itIn RSA examples, check that φ(p × q) = (p − 1)(q − 1).
Examples
φ(36)
Input: n 36
Result: 12
Prime 97
Input: n 97
Result: 96
Common Use Cases
- Checking number theory homework
- Studying how RSA works
- Counting reduced fractions with denominator n
Frequently Asked Questions (FAQ)
What is φ(1)?
1 (by convention 1 is coprime to itself).
Does it handle large numbers?
Yes, as long as the number can be factored; very large numbers can take a while.