Exp Calculator - Calculate e^x, ln(x) & Complex EXP

Calculate exp(x) as e raised to any real exponent, find x from a positive exponential value, or evaluate complex exponentials in radians or degrees.

Exp Calculator Formula

The calculator uses three formulas, selected through Solve for.

Real mode, forward direction:

exp(x) = e x

Real mode, inverse direction:

x = ln(y)

Complex mode (Euler's formula):

exp(a + bi) = e a \times (cos(b) + i \times sin(b))

e: Euler's number, approximately 2.718281828459045.
x: the real input exponent.
y: the value of exp(x), always positive.
a: the real part of a complex exponent.
b: the imaginary part, in radians or degrees.
ln: the natural logarithm, base e.

Select exp(x) from x, x from exp(x), or Complex exponential. Complex mode splits the exponent into magnitude e^a and angle b, then returns rectangular form. Degrees are converted to radians. Results use floating-point arithmetic; subnormal values and large angles can lose precision.

Reference Values and Range

Use these tables to sanity-check inputs before you trust a result.

x	exp(x)	Notes
-5	0.006738	Strong decay
-1	0.367879	1/e
0	1	Fixed point
1	2.718282	e
2	7.389056	e²
5	148.4132	Growth
10	22026.47	Five orders of magnitude
709.78	~1.793e+308	Upper limit before overflow

Complex input	exp result	Identity
0 + πi	-1	Euler's identity
0 + (π/2)i	i	Quarter rotation
0 + 2πi	1	Full rotation
1 + 0i	e	Pure real

Worked Examples

Example 1: Continuous interest. A balance grows at 4% per year compounded continuously for 7 years. The growth factor is exp(0.04 × 7) = exp(0.28). Select exp(x) from x and enter 0.28. The calculator returns about 1.32313. A starting balance of $5,000 becomes 5000 × 1.32313 = $6,615.65.

Example 2: Inverse problem. A bacteria culture grew by a factor of 12 under exponential growth. To find the exponent, select x from exp(x) and enter 12. The result is x = ln(12) ≈ 2.4849. If the elapsed time was 3 hours, the rate constant is 2.4849 / 3 ≈ 0.828 per hour.

FAQ

What is the difference between exp(x) and e^x? Nothing. They are two notations for the same function. "exp" is the spelled-out form used in programming and science.

Why does the calculator cap x near 709.78? Above that value, e^x exceeds the largest finite double-precision number (about 1.8 × 10³⁰⁸) and would return infinity.

Can exp(x) ever be negative or zero? No. For real x, exp(x) is always strictly positive. It approaches zero as x goes to negative infinity but never reaches it.

When should I use degrees instead of radians in Complex exponential mode? Use radians for math and physics work, since Euler's formula is defined that way. Use degrees only if your source data is already in degrees and you want the calculator to convert for you.