Power Modulo Calculator
Use our power modulo calculator (power mod calculator) to compute x^y mod n quickly. Includes what does modulo mean, how does modulo work, modulo examples, and the power modulo method used in modular arithmetic.
What Does Modulo Mean?
Modulo is an operation that returns the remainder after division. For example, 17 mod 5 = 2 because 17 ÷ 5 leaves a remainder of 2.
If you’re asking what does modulo mean or how does modulo work, it’s basically “what’s left over after dividing.”
Power modulo (also called modular exponentiation) is when you compute a power and then take the result modulo n, like x^y mod n. This shows up in number theory and many practical computing tasks.
Power Modulo Formula
Power modulo is the remainder when x^y is divided by n. In practice, modular exponentiation is used to keep numbers manageable.
r is the remainder after dividing x^y by n.
This lets you reduce intermediate values when computing large powers.
17 divided by 5 leaves remainder 2.
Compute the power, then take the remainder.
How to Use the Power Modulo Calculator
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Enter the base x.
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Enter the exponent y.
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Enter the modulus n.
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The calculator returns r = x^y mod n (the remainder).
Frequently Asked Questions
Modulo means the remainder after division. a mod n is the remainder when a is divided by n.
Divide a by n and take the remainder. Example: 14 mod 4 = 2 because 14 = 3·4 + 2.
10 mod 3 = 1, 20 mod 5 = 0, and 7 mod 2 = 1.
Power modulo is computing x^y mod n, the remainder when x raised to the power y is divided by n.
Because x^y can become extremely large. Modular exponentiation techniques compute the same remainder efficiently without storing huge numbers.
You can reduce x first: (x mod n)^y mod n gives the same result as x^y mod n, but you still apply mod n at the end.