Net Force Calculator

Work out net force instantly with clear inputs, formula shown and shareable results.

About Net Force Calculator

Forces add as vectors, so the resultant of two forces follows the parallelogram rule: sqrt(F1^2 + F2^2 + 2.F1.F2.cos theta). At right angles 40 N and 30 N give 50 N, not 70 N. Dividing by the mass gives the acceleration that resultant produces.

Formulas

Resultant magnitude

F = sqrt(F1^2 + F2^2 + 2 F1 F2 cos theta)

Direction

tan(phi) = F2 sin theta / (F1 + F2 cos theta)

Worked example

With the default values below, Net Force Calculator returns Resultant Force of 50.000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First forceminimum 0 N: 40 N
Second forceminimum 0 N: 30 N
Angle between the two forcesaccepts 0–180 deg: 90 deg
Mass being acted onminimum 0 kg: 10 kg

Results

Resultant Force: 50.000 N
Direction From The First Force: 36.87 deg
Resulting Acceleration: 5.0000 m/s2
Arithmetic Sum For Comparison: 70.00 N

Step by step

1Values used
2Resultant magnitude
3Direction
4Resultant Force= 50.000 N
5Direction From The First Force= 36.87 deg
6Resulting Acceleration= 5.0000 m/s2
7Arithmetic Sum For Comparison= 70.00 N

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is the resultant less than the arithmetic sum?

Because the forces do not point the same way. Only when the angle is zero do they add directly.

What if the forces oppose each other?

At 180 degrees the cosine is -1 and the resultant is the difference. Equal opposing forces give zero and the body stays in equilibrium.