All 12 Functions Supported
Calculate all six hyperbolic functions (sinh, cosh, tanh, coth, sech, csch) and all six inverse functions (arcsinh, arccosh, arctanh, arccoth, arcsech, arccsch) with full precision.
Compute sinh, cosh, tanh, coth, sech, csch and all inverse hyperbolic functions instantly. Upload CSV/TXT for bulk processing and export results in one click.
value | function or just value (uses default function above)| # | Function | Input (x) | Result | Formula | Type |
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Everything you need for fast, accurate hyperbolic function computation — from classroom to engineering.
Calculate all six hyperbolic functions (sinh, cosh, tanh, coth, sech, csch) and all six inverse functions (arcsinh, arccosh, arctanh, arccoth, arcsech, arccsch) with full precision.
All calculations run entirely in your browser — zero server round-trips, no data sent anywhere. Results appear in milliseconds even for thousands of bulk entries.
Process thousands of values in one go. Upload a CSV or TXT file with one value (and optional function name) per line and get all results instantly.
The calculator enforces domain restrictions in real time — for example, arccosh requires x ≥ 1 and arctanh requires |x| < 1. Invalid inputs are flagged before calculation.
As you type, see a live preview showing the function expression and the formula applied — so you always understand what is being computed.
Download results as a structured CSV file or copy them to clipboard in tab-separated format — ready for Excel, Google Sheets, MATLAB, or Python workflows.
Select the hyperbolic function you want — sinh, cosh, tanh, or any of the six inverse functions — using the function selector buttons.
Type your input value in the x field. Use any real number, positive or negative. Domain constraints are checked automatically in real time.
Hit the Calculate button. The result, formula used, and function type appear instantly in the results table below the calculator.
Use Copy, Download CSV, or Clear to save or share your hyperbolic function results — ideal for reports, spreadsheets, and data analysis.
Hyperbolic functions are a family of mathematical functions that bear striking similarities to the familiar trigonometric (circular) functions — but instead of being defined in terms of angles on a unit circle, they are defined using exponential expressions involving the unit hyperbola. The six core hyperbolic functions are sinh (hyperbolic sine), cosh (hyperbolic cosine), tanh (hyperbolic tangent), coth (hyperbolic cotangent), sech (hyperbolic secant), and csch (hyperbolic cosecant). Unlike their trigonometric counterparts, hyperbolic functions are not periodic — they grow or converge monotonically, making them uniquely suited to modelling exponential growth, catenary curves, and relativistic phenomena.
The two foundational functions are defined directly from Euler's number e: sinh(x) = (eˣ − e⁻ˣ) / 2 and cosh(x) = (eˣ + e⁻ˣ) / 2. All remaining functions derive from these two — for example, tanh(x) = sinh(x) / cosh(x), sech(x) = 1 / cosh(x), and csch(x) = 1 / sinh(x). This means a single exponential engine drives the entire family. For instance, sinh(1) ≈ 1.1752, cosh(1) ≈ 1.5431, and tanh(1) ≈ 0.7616.
The inverse hyperbolic functions — arcsinh, arccosh, arctanh, arccoth, arcsech, and arccsch — reverse the operation and are expressible in closed logarithmic form. For example, arcsinh(x) = ln(x + √(x²+1)), which is defined for all real x. By contrast, arccosh(x) = ln(x + √(x²−1)) is only valid for x ≥ 1, and arctanh(x) = ½ ln((1+x)/(1−x)) requires |x| < 1. Our calculator enforces all domain restrictions automatically.
Hyperbolic functions appear across engineering and science. The catenary curve — the shape formed by a hanging chain — is described by cosh(x). In special relativity, Lorentz boosts are expressed using cosh and sinh. In electrical engineering, transmission line equations rely on tanh and coth. In structural mechanics, the deflection of beams under distributed loads involves hyperbolic functions. Even machine learning has a connection — the hyperbolic tangent (tanh) is one of the most widely used activation functions in neural networks.
Our bulk upload feature makes it simple to evaluate hundreds or thousands of values at once. Format your CSV or TXT file with one value per line, optionally followed by a pipe (|) and the function name — for example 1.5 | tanh or -0.8 | arctanh. If you omit the function name, the calculator uses the default function you selected in the dropdown. All results are exportable as a clean CSV, ready to paste into Excel, Google Sheets, MATLAB, Python pandas, or any data analysis platform. Whether you are a student checking textbook answers, an engineer verifying load calculations, or a data scientist preprocessing features, this tool handles your entire workflow.
Hyperbolic functions are analogs of trigonometric functions, defined using the hyperbola rather than the unit circle. The six main functions — sinh, cosh, tanh, coth, sech, csch — are built from exponential expressions and appear throughout physics, engineering, and mathematics to model exponential growth, wave propagation, and geometric curves.
sin(x) is periodic and always oscillates between −1 and +1. sinh(x) = (eˣ − e⁻ˣ)/2 is not periodic — it grows without bound as x increases. Despite the similar notation, they behave very differently and arise in completely different contexts. sinh is an odd function like sin, but grows exponentially rather than oscillating.
Domain restrictions are: arccosh requires x ≥ 1; arctanh and arccoth require |x| < 1 and |x| > 1 respectively; arcsech requires 0 < x ≤ 1; arccsch requires x ≠ 0; arcsinh accepts all real numbers. Our calculator validates these constraints in real time and displays a clear error message for out-of-domain inputs before you calculate.
Yes. Upload a CSV or TXT file where each line contains a value, optionally followed by a pipe (|) and the function name. For example: 1.5 | tanh or simply 1.5 (uses your chosen default function). The calculator processes thousands of rows instantly, with domain validation on each line, and skips invalid entries gracefully.
Hyperbolic functions appear in the catenary shape of suspension bridge cables, special relativity and Lorentz transformations, AC transmission line analysis, fluid dynamics, differential equations for heat transfer, beam bending in structural engineering, and as the tanh activation function in neural networks and deep learning models.
Yes, completely free with no registration, no usage limits, and no data sent to any server. All calculations run locally in your browser, so your input values remain private. You can also save, copy, and download results at no cost.
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