Calculate e (Euler's number) raised to any power. Essential for exponential growth, decay, calculus, and scientific applications.
Last updated: April 2026 | By Patchworkr Team
Euler's number, denoted as e, is one of the most important mathematical constants, approximately equal to 2.71828. It is an irrational and transcendental number that forms the base of natural logarithms. Unlike π, which relates to circles and geometry, e emerges naturally from compound interest, continuous growth, and rates of change. The function f(x) = ex is unique in all of mathematics: its derivative (rate of change) is equal to itself. This self-referential property makes e the cornerstone of exponential functions and differential equations throughout science and engineering.
The constant e appears universally in nature's growth patterns: bacteria populations, radioactive decay, atmospheric pressure drop with altitude, and even the cooling of hot coffee following Newton's Law of Cooling. When things grow or decay at rates proportional to their current amount—whether populations, investments, or particles—the exponential function ex provides the exact mathematical description. Understanding ex is essential for physics, biology, economics, and any field modeling continuous change. The graph of ex always curves upward, reflecting exponential growth, while e-x curves downward, representing exponential decay.
Type any real number (positive, negative, or decimal) as your exponent x. For example, enter 2 to calculate e², or -1 to calculate e's reciprocal.
The calculator instantly computes e raised to your power using the exponential function. The result appears with multiple precision levels so you can choose the accuracy you need.
The output shows your result in multiple formats: rounded to 2 decimals for quick approximation, 4 decimals for standard precision, and scientific notation for very large or very small values.
Experiment with various inputs to observe how exponential growth behaves. Notice how large positive exponents give huge results, while negative exponents produce fractions less than 1.
Click the "Load Example" button to populate the calculator with x=2, which gives e² ≈ 7.39. This is a convenient starting point to verify the calculator's behavior.
Calculating continuous compound interest
e ≈ 2.71828... It's an irrational number that cannot be written as a simple fraction. It appears naturally in mathematics describing continuous growth and rates of change.
e<sup>x</sup> means e multiplied by itself x times (or raised to the power of x). For example, e<sup>2</sup> means e × e ≈ 7.39.
Because the exponential function e<sup>x</sup> perfectly describes processes that grow or decay at rates proportional to their current amount: population growth, radioactive decay, and cooling of objects.
Any number (except zero) raised to the power of 0 equals 1. Therefore, e<sup>0</sup> = 1. This is true for all exponential functions.
Natural logarithm (ln) is the inverse of the exponential function. If e<sup>x</sup> = y, then ln(y) = x. They undo each other.
Negative exponents produce reciprocals. For example, e<sup>-1</sup> = 1/e ≈ 0.368. Negative exponents model exponential decay.
Yes! Fractional exponents work perfectly. For example, e<sup>0.5</sup> ≈ 1.649 is the square root of e. Decimals work too.
Jacob Bernoulli discovered e while studying compound interest. Leonhard Euler popularized the notation 'e' in the 18th century, so it's now called Euler's number.
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