The Component Force 3D  calculator computes the component force along an axis based on the magnitude of the force and the angle between the vector and the axis.

INSTRUCTIONS: Choose units and enter the following:

• |`vecF`| Magnitude of Force Vector
• (θ) Angle Away from Vector

Component Force in 3D (F_z): The calculator returns the component force in Newtons.  However this can be automatically converted to compatible units via the pull-down menu.

To compute the angles from a 3D vector to the axes and the magnitude, CLICK HERE.

The Math / Science

This equation computes the component of a force in the direction of a coordinate specified in Euclidean three-space (3-Space).  In a standard local coordinate system specified by orthogonal coordinates x ,y, z this equation expresses the component of a force `vec F` that is exerted in the direction of one of the coordinate axes.

The equations for each component are

• `vec F_x` = `F cos(theta)`, where `theta` is the angle between the direction of the force, `vec F` and the x-axis
• `vec F_y` = `F * cos(phi)`, where `phi` is the angle between the direction of the force, `F` and the y-axis
• `vec F_z` = `F * cos(epsilon)`, where `epsilon` is the angle between the direction of the force, `F` and the z-axis

Notes

This equation can be used to represent any one of the three component forces that are the mapping of a vector force onto the local Euclidean 3-space coordinates

3D Vector Functions

• k⋅V - scalar multiplication
• V/k - scalar division
• V / |V| - Computes the Unit Vector
• |V| - Computes the magnitude of a vector
• U + V - Vector addition
• U - V - Vector subtraction
• |U - V| - Distance between vector endpoints.
• |U + V| - Magnitude of vector sum.
• V • U - Computes the dot product of two vectors
• V x U - Computes the cross product of two vectors
• V x U • W - Computes the mixed product of three vectors
• Vector Angle - Computes the angle between two vectors
• Vector Area - Computes the area between two vectors
• Vector Projection - Compute the vector projection of V onto U.
• Vector Rotation - Compute the result vector after rotating around an axis.
• Vector Components 3D - Returns a vector's magnitude, unit vector, spherical coordinates, cylindrical coordinates and angle from each axis.
• (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
• (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
• (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
• (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates
• (x,y) to (r, θ) - Cartesian to Polar
• (r, θ) to (x,y) - Polar to Cartesian 
• Vector Normal to a Plane Defined by Three Points