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What is resultant force?

The resultant force is the single force that has the same effect as all the forces acting on an object combined.

Resultant force explained

Forces in the same line add or subtract; forces at an angle combine with a vector triangle or by resolving into horizontal and vertical components.
A zero resultant means equilibrium. Equilibrium questions therefore reduce to two equations: the horizontal components balance and the vertical components balance.

Key formula

Fnet=Fx2+Fy2F_{\text{net}} = \sqrt{F_{x}^{2} + F_{y}^{2}}

Worked example

Forces of 3 N3\,\text{N} east and 4 N4\,\text{N} north give a resultant of 5 N5\,\text{N} at 53∘53^{\circ} to the east.

Examiner tip

Always draw the free-body diagram, even when it earns no explicit mark — it is the fastest way to spot a missing normal or friction force.

Resultant force: common questions

How do I find a resultant force at an angle?
Resolve each force into perpendicular components, add the components separately, then recombine using Pythagoras and trigonometry.
Can an object move with zero resultant force?
Yes — it moves at constant velocity. Zero resultant means no acceleration, not no motion.

Related terms

Newton's second law

Newton's second law states that the resultant force on an object equals its mass multiplied by its acceleration.

Moment of a force

The moment of a force is its turning effect about a pivot, equal to the force multiplied by the perpendicular distance to the pivot.

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