# e Calculator | eˣ | e Raised to Power of x

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Steven Wooding and Jack Bowater
Last updated: Nov 20, 2022

Are you solving an equation with Euler's number? Our e calculator is here to help! Our tool allows you to compute e to the power of any number you desire.

Keep on reading if you're still wondering what exactly Euler's number is, what does e mean on a calculator, and how to calculate e to the x 📐🧑‍🏫

🙋 You can also explore the exponential functions of other bases with our exponent calculator.

## What is e on a calculator? – e to the x

e is one of the most important constants in mathematics. We cannot write e as a fraction, and it has an infinite number of decimal places – just like its famous cousin, pi (π).

e has plenty of names in mathematics. We may know it as Euler's number or the natural number. Its value is equal to 2.7182818284590452353602… and counting! (This is where rounding and approximation become essential.) 🧮

Now that we know what e and its approximate value is, we can start thinking about its possible applications.

1. e is the base of the natural logarithm, the same you can find using natural log calculator.

2. We use e in the natural exponential function ( = e power x).

In the function, the slope of the tangent line to any point on the graph is equal to its y-coordinate at that point.

3. (1 + 1/n)ⁿ is the sequence that we use to estimate the value of e. The sequence gets closer to e the larger n is - but even if n = infinity, the sequence value is not equal to Euler's number.

We use this equation in compound interest calculations.

4. e is equal to the result of the following factorial equation:

$\scriptsize \qquad \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \ldots$
1. e is also a part of the most beautiful equation in mathematics: $e^{iπ} + 1 = 0$ 🌺

Since we already know what's the Euler's number, how about some other numbers we use in physics?

• Biot number;
• Knudsen number;
• Reynolds number; and
• f-number😀

🔎 To see the real-life applications of exponential functions, head to Omni's exponential growth calculator.

## How to put e in a calculator? Calculate e to the x

Since we're forced to use an approximation of e, we can simply input the value of e into any calculator.

How does it work in practice? How to calculate e to the power x?

If your calculator doesn't allow symbols, simply enter 2.718281828 (or any rounded form of this number) into your choice value box 👍

## e calculator – examples

In this section, we'll answer the very big question: "How to calculate e to the power eˣ?" using both our calculator and the traditional formula.

1. The e calculator – it's so simple it doesn't need further explanation. Enter the value of x into the text box and enjoy your results displayed alongside the step-by-step solution 👣

2. The traditional calculation requires you to choose how many decimal places of the Euler's number you will use.

We decided to use 9 decimal places.

We know that the area up to any x-value is also equal to eˣ:

We'd love to calculate the area up to the e¹⁰ function.

• e¹⁰ = 2.718281828¹⁰;

• 2.718281828¹⁰ = 2.718281828 × 2.718281828 × 2.718281828 × …;

• 2.718281828¹⁰ = 22026.47.

And this is how to calculate e to the power of 10.

As you can see, calculating e to the power of x might be pretty troublesome and time-consuming - our tool is a simple solution for that unnecessary problem 🤗

## FAQ

### What does exp mean?

"Exp" is short for "exponential" and is used in the notation exp(x) as another way to write eˣ.

### How do you calculate e to the power x without calculator?

You can use the following Taylor series approximation: eˣ = 1 + x + x²/2! + x³/3! + …. Continue calculating and adding terms to get a better approximation.

### What is e to the negative infinity?

Zero. Let's say we have e-N, where N is a large number tending toward infinity. Now, given that e-N = 1/eN, as N gets larger, e-N will get smaller, ending up at zero if N = ∞.

### What is the derivative of e to the x?

The derivative of eˣ is itself, eˣ. Here is a step-by-step proof:

1. The equation y = eˣ can be rewritten as ln y = x.
2. Differentiate both sides of this equation and use the chain rule:
1/y × dy/dx = 1
dy/dx = y
3. Since y = eˣ, therefore dy/dx = eˣ.
Łucja Zaborowska, MD, PhD candidate Result (eˣ)
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