Force Vector Addition

The Force Vector Addition calculator computes the magnitude of a resulting force based on two forces and the angle between them.

INSTRUCTIONS:  Choose units and enter the following:

• (A) Magnitude of Vector A
• (B) Magnitude of Vector B
• (θ) Angle between Vectors A and B

Result Vector (C): The calculator returns the magnitude of vector C in Newtons and the angle (α) in degrees.  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

• Compute Vector Magnitude (CLICK HERE)
• Compute the Angle between Two Vectors (CLICK HERE)

The formula for the addition of two force vectors is:

    `|C| = sqrt( (B sin(θ))^2 + (A + B cos(θ))^2)` 

      α = asin( y / C)    

where:

• α is the resulting vector angle
• y is the resulting vector vertical offset
• C is the sum of the two force vectors
• A is the first force vector
• B is the second force vector
• θ is the angle between them.

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