Hyperbola Calculator
Compute eccentricity, foci, vertices and asymptotes of a hyperbola from a and b.
About Hyperbola Calculator
For the standard hyperbola x²/a² − y²/b² = 1, the foci are at (±c, 0) where c = √(a²+b²). Eccentricity e = c/a is always > 1. Asymptotes are y = ±(b/a)x.
Formulas
Focal Distance
c = √(a² + b²)
- a
- Semi-transverse axis
- b
- Semi-conjugate axis
Eccentricity
e = c / a
- c
- Focal distance
- a
- Semi-transverse axis
Worked example
With the default values below, Hyperbola Calculator returns Eccentricity of 1.166190. Change any input above and every figure here is recalculated in your browser.
Inputs used
- a (semi-transverse axis)minimum 0
- 5
- b (semi-conjugate axis)minimum 0
- 3
Results
- Eccentricity
- 1.166190
- Focal Distance (c)
- 5.8310 units
- Vertex (±a)
- 5.0000 units
- Asymptote Slope (±b/a)
- 0.6000
Step by step
- 1Focal distance= 5.8310
- 2Eccentricity= 1.166190
- 3Asymptote slopes
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is a hyperbola different from an ellipse?
An ellipse has c² = a² − b² (e < 1), while a hyperbola has c² = a² + b² (e > 1). A hyperbola has two separate branches.
What are the asymptotes?
The lines y = (b/a)x and y = −(b/a)x that the hyperbola approaches but never touches.