Hyperbolic Sine Calculator (sinh)

sinh(x) = (eˣ − e⁻ˣ) / 2. Hyperbolic counterpart of sin.

Inputs

Result

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How to use this calculator

  • Enter x.
  • Read sinh(x) + e^x components.

About this calculator

Hyperbolic sine: sinh(x) = (eˣ − e⁻ˣ) / 2. Like its trig cousin, sinh is an odd function (sinh(−x) = −sinh(x)) and grows roughly exponentially. Key identity: cosh²(x) − sinh²(x) = 1. Used in physics (catenary curve = a cosh(x/a) describes a hanging chain), engineering (suspension cables), and special relativity.

Frequently asked

How is sinh different from sin?+
sin is bounded [−1, 1] and periodic. sinh is unbounded and grows like eˣ/2 for large x. Different curves entirely.
cosh² − sinh² = 1?+
Yes — analogous to cos² + sin² = 1 but with a sign change. Hyperbolic vs. circular trig.
What's a catenary?+
The shape of a hanging chain or cable: y = a cosh(x/a). Visually similar to a parabola but mathematically different.
sinh in special relativity?+
Velocity addition uses tanh; rapidity is the hyperbolic angle. Lorentz boosts are hyperbolic rotations.
Inverse?+
sinh⁻¹(x) = ln(x + √(x² + 1)) = arcsinh(x). Defined for all real x.

Related calculators

Hyperbolic Cosine Calculator (cosh)
cosh(x) = (eˣ + e⁻ˣ) / 2. Catenary curve: y = a · cosh(x/a).
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tanh(x) = sinh(x) / cosh(x). Bounded between −1 and 1. Used in neural networks.
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