Example 1 — one
- Exponent: 1
about 2.718
That is the number e itself.
Exponential function eˣ
Enter an exponent x — we compute e raised to that power. e is a special number (about 2.718) used a lot in school math.
This is not any base — only the number e. 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 e (about 2.718) and raise it to the power x.
At x = 0 the result is always 1. At x = 1 you get e itself. At x = 2 you get e×e. A negative x gives a fraction: e⁻¹ is 1/e.
This is not the same as “2 to the power x” or “10 to the power x”. The base is fixed: e. For another base, use a power calculator.
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 it
- Enter the exponent x — fractions and negatives are fine.
- Read eˣ.
- If a very negative x is “too small to show”, try a milder value or treat the result as practically zero.
Examples
Example 2 — zero
- Exponent: 0
1
e to the power 0 is 1.
Example 3 — negative exponent
- Exponent: −1
about 0.368
That is 1/e — positive and less than 1.
FAQ
What is the number e?
A math constant, about 2.718. It shows up with exponential growth and many school formulas.
Can the result be negative?
No. eˣ is always greater than zero.
What does a negative exponent mean?
You get a reciprocal: e⁻x = 1 / eˣ. Still positive, but less than 1 when x > 0.
Why does a large x explode?
Powering a base bigger than 1 grows fast. That is exponential growth.
How is this different from a logarithm?
eˣ goes one way (exponent → value). The natural log goes the other way (value → exponent).
Can I enter a fraction like 0.5?
Yes. e⁰·⁵ is the square root of e.
Why do I get a message for a very negative x?
The result is so close to zero that ordinary browser math cannot show it. It is not negative.
Is this the same as 2ˣ?
No. The base here is e, not 2. Use a power calculator for another base.