e Calculator | ex | e Raised to Power of x
Calculate Euler's number e (≈ 2.71828) raised to any power
Enter the power to raise e (≈ 2.71828) to
How to Use This Calculator
Enter the Exponent
Input the power (x) to which you want to raise Euler's number e. This can be any real number: positive, negative, or zero.
Calculate
Click "Calculate e^x" to compute Euler's number raised to your specified power. The result will be displayed in both standard and scientific notation.
View Results
Review the calculated result. For very large or very small numbers, scientific notation is automatically used for clarity.
Formula
ex = exp(x)
Where:
- e = Euler's number ≈ 2.718281828459045...
- x = exponent (any real number)
- ex = e raised to the power of x
Example 1: e¹
e¹ = e ≈ 2.71828
Example 2: e²
e² ≈ 2.71828² ≈ 7.38906
Example 3: e⁰
e⁰ = 1 (any number to the power 0 equals 1)
Example 4: e⁻¹
e⁻¹ = 1/e ≈ 0.36788
Example 5: e⁻²
e⁻² = 1/e² ≈ 0.13534
About e Calculator
The e Calculator computes Euler's number (e) raised to any power. Euler's number e ≈ 2.71828 is a fundamental mathematical constant that appears naturally in many areas of mathematics, especially in calculus, exponential growth, and complex analysis. The function ex is the exponential function and is its own derivative, making it crucial in differential equations and mathematical modeling.
When to Use This Calculator
- Calculus: Calculate exponential functions and their derivatives/integrals
- Compound Interest: Calculate continuous compounding: A = Pert
- Exponential Growth/Decay: Model populations, radioactive decay, or bacterial growth
- Statistics: Calculate probabilities in exponential distributions
- Physics: Solve problems involving exponential decay, RC circuits, or wave functions
Why Use Our Calculator?
- ✅ Instant Results: Get accurate e^x calculations immediately
- ✅ High Precision: Uses JavaScript's Math.exp() for maximum accuracy
- ✅ Scientific Notation: Automatically displays very large/small numbers in scientific notation
- ✅ Easy to Use: Simple interface for all skill levels
- ✅ 100% Free: No registration or payment required
- ✅ Educational: Learn about Euler's number and exponential functions
Common Applications
Finance - Continuous Compounding: If you invest $1,000 at 5% annual interest compounded continuously for 3 years: A = 1000 × e0.05×3 = 1000 × e0.15 ≈ $1,161.83.
Biology - Population Growth: If a bacterial population grows continuously at rate r, the population after time t is P(t) = P₀ × ert, where P₀ is the initial population.
Physics - Radioactive Decay: The amount of radioactive material after time t is N(t) = N₀ × e-λt, where λ is the decay constant and N₀ is the initial amount.
Calculus - Natural Logarithm: The natural logarithm ln(x) is the inverse of ex. If ey = x, then y = ln(x).
Tips for Best Results
- Remember: e⁰ = 1 (any number to power 0 is 1)
- Remember: e¹ = e ≈ 2.71828
- For negative exponents: e-x = 1/ex
- Large positive exponents give very large results
- Large negative exponents give values close to zero
Frequently Asked Questions
What is Euler's number e?
Euler's number e ≈ 2.71828 is an irrational mathematical constant that appears naturally in exponential growth, calculus, and many areas of mathematics. It's the base of the natural logarithm and has the unique property that the function ex is its own derivative.
What is e raised to the power of 0?
e⁰ = 1. Any number (except 0) raised to the power of 0 equals 1. This is a fundamental rule of exponents.
What is e raised to the power of 1?
e¹ = e ≈ 2.71828. This is the definition of e - when e is raised to the first power, it equals itself.
What about negative exponents?
Negative exponents represent reciprocals: e-x = 1/ex. For example, e⁻¹ = 1/e ≈ 0.36788, and e⁻² = 1/e² ≈ 0.13534.
Where is ex used in real life?
ex is used in continuous compound interest calculations, exponential growth/decay models (populations, radioactive decay), RC circuits in electronics, probability distributions in statistics, and solving differential equations in physics and engineering.