Quick answer
The net force is the vector sum of the forces: Rₓ = ΣF cos θ, R_y = ΣF sin θ and |R| = √(Rₓ² + R_y²). Two 10 N forces at 0° and 90° have a net force of 14.14 N at 45°.
Enter the force magnitudes and their directions in degrees. The calculator returns the net force and its direction.
Related tools: Force Calculator: Force from mass and acceleration (Newton's second law). Centripetal Force Calculator: Force and acceleration for circular motion. Normal Force Calculator: Normal force on an object resting on a flat or inclined surface.
How to use the Net Force Calculator
- Type force magnitudes (N), for example 50, 30, 20.
- Type direction of each force (° from the x-axis), for example 0, 120, 240.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Force magnitudes (N) | Text, such as 50, 30, 20 | — |
| Direction of each force (° from the x-axis) | Text, such as 0, 120, 240 | — |
Formula and method
Formula
Rₓ = ΣF cos θ, R_y = ΣF sin θ, |R| = √(Rₓ² + R_y²)
IEEE-754 double precision; shown to the decimals indicated.
Direction measured counter-clockwise from the +x axis, 0–360°.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Force magnitudes (N) = 10, 10; Direction of each force (° from the x-axis) = 0, 90.
| Result | Value |
|---|---|
| Net force | 14.142136 N |
| Direction | 45° |
Example 2
Inputs: Force magnitudes (N) = 50, 30, 20; Direction of each force (° from the x-axis) = 0, 120, 240.
| Result | Value |
|---|---|
| Net force | 26.457513 N |
| Direction | 19.1066° |
Example 3
Inputs: Force magnitudes (N) = 100, 40; Direction of each force (° from the x-axis) = 30, 210.
| Result | Value |
|---|---|
| Net force | 60 N |
| Direction | 30° |
The first line is the headline result (net force). Below it the net Force Calculator lists direction, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Worked example
Rₓ = 10 cos 0° + 10 cos 90° = 10 and R_y = 0 + 10 = 10. |R| = √200 = 14.142 N and the direction is arctan(10 ÷ 10) = 45°.
Equilibrium
If the net force is zero, the object is in equilibrium. Three 10 N forces at 0°, 120° and 240° balance. Lists of magnitudes and directions must be the same length.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Direction of each force (° from the x-axis): entering "0" shows "Enter one angle for every force." beside that field and no result.
- Force magnitudes (N): left empty shows "Enter force magnitudes (n)." beside that field and no result.
Choosing between the Net Force Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Force Calculator](/science/force-calculator/) | mass and acceleration | Force |
| [Centripetal Force Calculator](/science/centripetal-force-calculator/) | mass, speed and radius | Centripetal force |
| [Normal Force Calculator](/science/normal-force/) | mass, incline angle and gravitational acceleration | Normal force |
| [Friction Force Calculator](/science/friction-force-calculator/) | coefficient of friction μ and normal force | Friction force |
| [Momentum Calculator](/science/momentum-calculator/) | mass and velocity | Momentum |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Lists must be the same length
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for direction of each force (° from the x-axis) and force magnitudes (N) to confirm this.
Frequently asked questions
What if forces are opposite?
Opposite forces subtract: 10 N right and 6 N left give a net 4 N to the right.
What if the net force is zero?
With zero net force, an object keeps its velocity: it stays at rest or moves at constant speed in a straight line.
How many forces can I add?
As many as you list.
What does the Net Force Calculator calculate?
Resultant of several forces at different angles. It returns Net force and Direction.
What formula does the Net Force Calculator use?
Rₓ = ΣF cos θ, R_y = ΣF sin θ, |R| = √(Rₓ² + R_y²). Direction measured counter-clockwise from the +x axis, 0–360°.
What do I need to enter in the net Force Calculator?
You enter Force magnitudes (N) and Direction of each force (° from the x-axis).
What is an example of a net Force result?
With force magnitudes (N) 10, 10 and direction of each force (° from the x-axis) 0, 90, the net force is 14.142136 N.
Related calculators
- Force Calculator — Force from mass and acceleration (Newton's second law).
- Centripetal Force Calculator — Force and acceleration for circular motion.
- Normal Force Calculator — Normal force on an object resting on a flat or inclined surface.
- Friction Force Calculator — Friction force from the coefficient of friction and the normal force.
- Momentum Calculator — Linear momentum from mass and velocity.
- Coefficient of Friction Calculator — Coefficient of friction from friction and normal forces.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.