Resultant of two forces
Components at right angles.
Method
Worked case: 3 and 4 is a resultant of 5 at 53.13° from the x-axis.
What to write beside the result
A review can only check this figure if the inputs sit next to it. Write the value, the unit and the assumption the form used. A diameter in millimetres and a diameter in metres are not the same reading. A force in kilonewtons divided as if it were newtons is a thousand-fold error.
The result is the arithmetic on this page. It is not a utilisation, not a selected product, and not a clause from a standard. If the number is going into a shared container, name the page, the date and the inputs. The file-name checker does not read the calculation.
Logic: how this figure is built.
How to read a resultant
This page answers a statics question: two perpendicular components, what single force replaces them and at what angle to the x-axis. The magnitude is the square root of the sum of squares. The angle is the arctangent of y over x.
Components 3 and 4 give a resultant of 5 at 53.13° from the x-axis. That is the 3-4-5 triangle. The angle is from the positive x-axis toward the positive y-axis. A negative component moves the angle into another quadrant. The page is not a general vector sum of forces at odd angles.
Both components need the same unit. A 3 kN force and a 4 N force are not a 5 kN resultant. Concurrent forces that are not perpendicular need a resolution into axes first. This page assumes you have already done that.
Use it to check a hand resolution before it is typed into a model. It does not find reactions, it does not apply a load factor, and it does not say whether the member can carry the resultant.
- Related: beam reactions
- structural logic
Last checked 3 October 2026. See the disclaimer.