Calculadora de Funções Hiperbólicas
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
senh(x) = (eˣ − e⁻ˣ)/2 ; cosh(x) = (eˣ + e⁻ˣ)/2
About this calculator
The hyperbolic functions calculator computes sinh(x), cosh(x), and tanh(x) for any real number x. These functions are analogous to trigonometric functions but based on the hyperbola instead of the circle. They are widely used in engineering, physics, and applied mathematics.
The calculation follows directly from the definitions: sinh(x) = (e^x - e^(-x))/2, cosh(x) = (e^x + e^(-x))/2, and tanh(x) = sinh(x)/cosh(x). The calculator uses high-precision numerical approximations for the exponential, ensuring reliable results for typical x values.
Use this calculator when dealing with problems involving hanging cables (catenaries), wave propagation, special relativity, or electrical circuits. It is also helpful for integrals and differential equations involving hyperbolic functions.
Caution: for very large x (above 700), computing e^x may cause numerical overflow. The calculator handles this by returning infinity. Also, note that cosh(x) is never less than 1, and tanh(x) approaches ±1 for large x.
Frequently asked questions
What is the difference between hyperbolic and trigonometric functions?
Hyperbolic functions are based on the hyperbola, while trigonometric functions are based on the circle. Despite similar names, their properties and applications differ.
In what real situations are hyperbolic functions used?
They appear in hanging cables (catenaries), wave propagation on strings, special relativity, and AC electrical circuits.
Can I use this calculator for complex numbers?
No, this calculator only accepts real numbers. For complex numbers, you need specific tools.
What does overflow mean and how to avoid it?
Overflow occurs when the number is too large to represent. Avoid x values above 700 for exponentials, or use scientific notation carefully.
Does the calculator provide inverse functions?
No, only sinh, cosh, and tanh. For inverses (arsinh, arcosh, artanh), you need another calculator.