Euler Formula Calculator

Use our free Euler formula calculator to evaluate e^(iθ) = cosθ + i·sinθ, explore Euler's identity, special angle values, cis(θ), and general complex exponentials e^(a+bi).

Math

Mode

θ (radians)

Real part a

Imaginary part b

Formula

Explore Euler's formula e^(iθ) = cosθ + i·sinθ. Evaluate at any angle, view special values at common angles, explore Euler's identity e^(iπ)+1=0, use cis(θ) notation, and compute general complex exponentials e^(a+bi).

e^(iθ) = cos(θ) + i·sin(θ)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter θ in radians (or choose special values mode).
2Select mode: evaluate, special, identity, cis, or complex-exp.
3For complex-exp: enter real part a and imaginary part b.
4Click Calculate.

Examples

e^(iπ)

1.cos(π) = −1
2.sin(π) = 0
3.e^(iπ) = −1

Result: -1

Euler's Identity

1.e^(iπ) + 1 = 0

Result: -1

Frequently Asked Questions

e^(iθ) = cos(θ) + i·sin(θ) — connects exponential functions to trigonometry.

e^(iπ) + 1 = 0 — considered the most beautiful equation in mathematics.

cis(θ) = cos(θ) + i·sin(θ) = e^(iθ), a shorthand notation.

e^(a+bi) = e^a · (cos(b) + i·sin(b)).

Always 1 — it lies on the unit circle in the complex plane.

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CalculateMe Team

Last updated: 2026-07-15

Euler Formula Calculator

Formula

How It Works

Examples

e^(iπ)

Euler's Identity

Frequently Asked Questions

What is Euler's formula?

What is Euler's identity?

What is cis(θ)?

What is e^(a+bi)?

What is |e^(iθ)|?

Related Calculators

Euler Formula Calculator

Formula

How It Works

Examples

e^(iπ)

Euler's Identity

Frequently Asked Questions

What is Euler's formula?

What is Euler's identity?

What is cis(θ)?

What is e^(a+bi)?

What is |e^(iθ)|?

Related Calculators