Example 1
- Exponent: 1
about 2.718
That is the number e itself.
Exponential function eˣ calculator
Type the exponent x. The base is fixed: the number e, about 2.718. e¹ is e itself, e⁰ is 1, e² is e times e, about 7.389. For a large negative x the result nears zero and stays positive.
Only the number e, not an arbitrary base. eˣ is always positive. A large positive x makes a huge result. A large negative x moves toward zero, but never below zero.
Result
Enter an exponent to see the result.
What it means
eˣ means: take the number e (about 2.718) and raise it to the power x. At x = 0 the result is always 1. At x = 1 the result is e itself. At x = 2 it is e×e, about 7.389. For negative x you get a fraction: e⁻¹ is 1/e, about 0.368.
Only base e, not 2 or 10. 2¹⁰ = 1024 lives on power. log base e of a number lives on logarithm when you type base e. The result eˣ is always positive. For a large positive x it grows fast.
One Exponent field. Type 1, click Calculate. A comma and a period both parse. x may be a fraction. If a very negative x is too small to show, shrink |x| or treat it as practically zero, still positive.
Power with base 10 and exponent 2 gives 100, a different pair. The square root of e is e to the 1/2, about 1.649, still this calculator when you type 0.5.
Without an exponent, nothing computes. 1 still gives about 2.718 no matter the header.
e³ ≈ 20.086. e⁻² ≈ 0.135. e^0.5 ≈ 1.649. Check 1 and 0 on the page.
Where it helps
- Lessons on the exponential function and the number e.
- Checking homework that uses eˣ.
- Comparing exponential growth with linear growth.
- Simple school models of continuous growth.
How to use
- Type the exponent x in Exponent, for example 1, 0, or −1.
- Click Calculate. x = 1 gives about 2.718. x = 0 gives 1. x = 2 gives about 7.389.
- A fraction and a minus both run. e to the −1st is about 0.368.
- A very negative x pushes the result toward zero from above. The result does not go below zero.
- Another base, 2 or 10, lives on power. The inverse of eˣ at base e lives on logarithm.
eˣ at x = 1 and x = 0
The exponential here is eˣ, base e with no field. e¹ ≈ 2.718. e⁰ = 1. e² ≈ 7.389. The result is always positive.
- e
- The base, about 2.718. Not 2 and not 10. On power you type the base yourself.
- x
- The exponent. 1, 0, 2 or −1. A large negative x damps the result toward zero from above.
Examples
Example 2
- Exponent: 0
1
e to the power 0 is 1.
Example 3
- Exponent: −1
about 0.368
That is 1/e - positive and less than 1.
Example 4
- Exponent: 0
1
What is e to the 0? 1. e to the 1 is about 2.718 on a second run.
Related calculators
FAQ
What is e to the 1st?
The result is about 2.718. That is e itself. First example on the page, not 2¹ and not 10¹.
What is e to the 0th?
The result is 1. Any positive base to the power 0 is 1. e is no exception.
What are e to the 2nd and e to the −1st?
About 7.389 and 0.368. The second is 1/e. e² is e times e, e⁻¹ is the reciprocal of e.
Can the result be negative?
No. eˣ is always positive. A large negative x only pulls the result toward zero, it does not cross to minus.
How is this different from 2 to the x?
Here the base is e, one field. 2¹⁰ = 1024 lives on the power page, with a base and an exponent.
What is e to the 0.5?
About 1.649. That is the square root of e, because e^(1/2). Not 0.5 × e.
What is e³?
About 20.086. e⁻² is about 0.135. Three factors of e, or 1/e².
Where do I invert eˣ?
On the natural logarithm. ln e = 1, ln e² = 2. Here the unknown is eˣ, there it is x.
Can I type 10 as the exponent?
Yes. e¹⁰ is huge, about 22026. The calculator still computes e to the x, not 10 to the x.
What if the result is too small to show?
Shrink |x| or treat it as practically zero. It is still positive, not negative.
Knowledge sources
The calculator computes the same formula as the definition below.
- Wikipedia — exponential function
- MathWorld — exponential function
- NIST DLMF 4.2 — exponential function
Page updated in 2026.