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`L = f(a,b)`

Enter a value for all fields

The **Arc Length of a Parabola** calculator computes the arc length of a parabola based on the distance (a) from the apex of the parabola along the axis to a point, and the width (b) of the parabola at that point perpendicular to the axis.

**INSTRUCTIONS:** Choose units and enter the following:

- (
**a**) Length Along Axis (from the apex along the axis to the chord) - (
**b**) Length of Chord

**Arc Length (L)**: The calculator returns the length in meters. However, this can be automatically converted to other length units via the pull-down menu.

The formula for the arc length of a parabola is:

`L = 1/2 sqrt(b^2 + 16*a^2) + b^2/(8*a) ln((4*a+sqrt(b^2+16*a^2))/b)`

where:

- L is the length of the parabola arc
- a is the length along the parabola axis
- b is the length perpendicular to the axis making a chord.

**Parabola Formula**: This computes the y coordinate of a parabola in the form y = a•x²+b•x+c**Parabolic Area**: This computes the area within a section of a parabola**Parabolic Area (Concave)**: This computes the outer area of a section of a parabola.**Parabolic Arc Length**: This computes the length a long a segment of a parabola.**Paraboloid Volume**: This is the volume of a parabola rotated around an axis (i.e. paraboloid)**Paraboloid Surface Area**: This is the surface area of a paraboloid.**Paraboloid Weight**: This is the weight or mass of a paraboloid.**Ballistic Flight Parabolic Equation**: This provides the formula of the parabola that matches a ballistic flight.

- “Segment of a Parabola (4.25).”
*Mathematical Handbook*, by Murray R Spiegel, 36th ed., McGraw Hill, 1997.