How this calculation works
Find hyperbolic distance in the Poincaré upper half-plane model.
THE FORMULA
d=2 asinh(|P−Q|/(2√(y₁y₂)))A worked example
On a vertical line, heights 1 and 2 are separated by ln 2.
Good to know
Both heights must be positive.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Find hyperbolic distance in the Poincaré upper half-plane model.
The primary result is labeled “Hyperbolic distance”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Both heights must be positive.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
On a vertical line, heights 1 and 2 are separated by ln 2.
Which rule does this calculator apply?
d=2 asinh(|P−Q|/(2√(y₁y₂)))