e^x Calculator: Compute e to Power x Fast

e to the x

Compute e^x instantly – the natural exponential base raised to any power

Enter x value:

ex

Decimals:

2.71828

Switch to ln(y) → x

e^x Graph (-5 to 5)

Hover or tap to highlight point • Drag to zoom

Common e^x Values

x	e^x (10 decimals)
0	1.0000000000
1	2.7182818285
2	7.3890560989
π	23.1406926328
-1	0.3678794412
10	22026.4657948

Core Formulas

Power Series

e^x = ∑(xⁿ / n!) from n=0 to ∞

Steps for x=1 (first 5 terms)

1 + 1/1! = 2
+ 1²/2! = 2.5
+ 1³/3! ≈ 2.666
+ 1⁴/4! ≈ 2.708
+ 1⁵/5! ≈ 2.717

Limit Form

e^x = lim (1 + x/n)ⁿ as n→∞

Steps for x=1, n=1000

(1 + 1/10)¹⁰ ≈ 2.5937
(1 + 1/100)¹⁰⁰ ≈ 2.7048
(1 + 1/1000)¹⁰⁰⁰ ≈ 2.7169
Approaches 2.71828…

Growth Comparison

Left: y=e^x (real) • Right: |e^(x+iy)| for y=1 (magnitude spirals out)

Compound Interest Example

Principal ($): Rate (%/year): Years:

Amount: $0

Formula: A = P * e^(rt) for continuous compounding

Frequently Asked Questions

What equals e^0?

Any number to the power 0 equals 1, so e^0 = 1 exactly.

Derivative of e^x?

The derivative is e^x itself – d/dx [e^x] = e^x.

e^x as x → -∞?

e^x approaches 0, serving as the x-axis asymptote.

exp(x) vs e^x notation?

Both mean the same: exp(x) = e^x, where e ≈ 2.71828.

References

Omni Calculator. “e Calculator | e^x | e Raised to Power of x”. Accessed December 2025.
Wikipedia. “Exponential function”. Accessed December 2025.
Reddit r/calculus. “What is e^x?”. Discussion thread, November 2024.