Force Vector Addition (angle)

$C = f( "A" , "B" , theta )$

Enter a value for all fields

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

INSTRUCTIONS: Choose units and enter the following:

(A) The magnitude of vector A
(B) The magnitude of vector B
(θ) The angle between vectors A and B

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

The Math / Science

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.
(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
Vector Normal to a Plane Defined by Three Points