How this calculator works
A force is a vector, so magnitudes alone cannot be added unless all forces share a direction. Resolve each force into perpendicular components, sum each column, then reconstruct magnitude and angle. A component table shows each contribution. Tiny roundoff components below 10^-14 of the summed input magnitudes are set to zero, so exactly opposed forces have no reported direction.
Formula
Fx = sum(Fi cos(theta_i)); Fy = sum(Fi sin(theta_i)); F = sqrt(Fx²+Fy²); theta = atan2(Fy,Fx).
Worked example
A 3 N force at 0 degrees and 4 N at 90 degrees give Fx = 3 N, Fy = 4 N and magnitude 5 N, directed 53.1301 degrees from positive x.
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Frequently asked questions
Can I use negative magnitudes?
Use a nonnegative magnitude and rotate the angle by 180 degrees to reverse a force.
What angle units does the text field use?
Always degrees. The angle output selector can display the result in radians or degrees.
Why does a zero resultant have no angle?
A vector with zero magnitude has no unique direction.