Net Force Calculator – Two Forces
Add two forces in a plane using their magnitudes and directions.
Formula
Fₓ = ΣF cos θ; Fᵧ = ΣF sin θ; |F| = √(Fₓ² + Fᵧ²)
First force: 3 N · Second force: 4 N · Horizontal component ≈ (3 N)×(1)+(4 N)×(0) · Vertical component ≈ (3 N)×(0)+(4 N)×(1) · Resultant magnitude ≈ sqrt((3)^2+(4)^2)
How to use
- Enter each force magnitude.
- Enter angles counterclockwise from the positive x axis.
- Read the resultant magnitude and signed components.
Examples
- 3 N right and 4 N up give a resultant magnitude of 5 N.
Frequently asked questions
How is direction represented?
By the signed x and y components, not a polar angle.
What if the resultant is zero?
The forces balance; the zero vector has no direction.
Can this include more than two forces?
Combine forces into two groups first, or use a vector calculation for the full system.
How are cardinal directions handled?
Sine and cosine factors are rounded to 15 decimal places so axis-aligned forces cancel exactly.
Sources
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