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`y = a*x^2 + b*x + c`

Enter a value for all fields

The **Ballistic Flight Parabolic Equation** calculator computes the parabolic equation coefficients based on the launch angle above the horizon (**θ**) at an initial velocity (**V**) assuming a constant downward acceleration (**g**).

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

- (
**V**) Initial Launch Velocity - (
**θ**) Launch Angle above the horizon. - (
**g**) Acceleration due to gravity (default is 9.80665 m/s^{2})

**Parabolic Flight Equation**: The calculator returns the equation of the parabola to match the flight. It also returns the maximum ballistic range and max height achieved.

The formula for the parabolic flight equation is:

y = a•x² + b•x + c

where:

- a = -4 • M / R²
- b = 4 • M / R
- c = h (initial height)
- M is the Ballistic Maximum Altitude without h
- R is the Ballistic Maximum Range without h

The addition of the initial height (h) to the Max Altitude and Range have the effect of shifting the parabola to the right, when all that is wanted is a shift up.

One of the most common representations of a parabola in nature is an object moving in the gravitational field of a massive body, such as the projectile motion of a body affected by the Earth's gravity. The figure shows the parabolic trajectory typifying a projectile that is affected solely by gravity, **g**.

- Ballistic Maximum Altitude: This is the maximum altitude achieved in free ballistic flight.
- Ballistic Maximum Range: This is the maximum horizontal range.
- Ballistic Flight Time: This is the time duration of free flight.
- Simplified Ballistic Range: This is the range with no initial elevation above the plane.
- Ballistic Vertical Velocity: This is the vertical velocity at a given time.
- Ballistic Horizontal Velocity: This is horizontal velocity or ground speed.
- Vertical Position (Y) in Ballistic Flight: This compute the vertical position (y) at a given time within ballistic flight.
- Horizontal Position (X) in Ballistic Flight: This compute the horizontal position (x) at a given time within ballistic flight..
- Ballistic Position at Time (t): This compute the position (x,y) at a given time within ballistic flight, where x is distance down range and y is the height above the plane.
- Ballistic Parabolic Equation provides the parabolic flight position equation based on the launch speed, height and angle.
- Acceleration Due to Gravity at Sea Level
- Velocity to achieve a Max Ballistic Height: This computes the initial velocity required to achieve the max height.
- International Gravity Equation
- Force of Earth's Gravity
- Force of Drag

**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.

[Figure] Initial velocity of parabolic throwing

Source: Wikipedia / Fizped (modified to include motion equation)

URL: http://en.wikipedia.org/wiki/Projectile_motion#mediaviewer/File:Ferde_hajitas1.svg