This is a browser-based vector resultant calculator for undergraduate statics and engineering courses. Add 2D or 3D force vectors by dragging from the origin on the canvas, or type exact magnitudes and angles directly in the sidebar. The resultant force magnitude, direction angle, and Cartesian components update instantly. Export the diagram and results table as PNG to paste into Word, or download as PDF. No account, no watermark, no paywall.
The tool runs entirely in your browser. Nothing leaves your computer.
Ctrl+Z and Ctrl+Y undo and redo. The Clear button resets the canvas.
When two or more force vectors act on the same point, their combined effect is represented by a single equivalent force called the resultant. The resultant has the same magnitude and direction as the vector sum of all the individual forces.
To find the resultant analytically, resolve each force into its x and y components, sum all x-components and all y-components separately, then combine:
|R| = sqrt((SumFx)^2 + (SumFy)^2) and theta = atan2(SumFy, SumFx)
The angle is measured counterclockwise from the positive x-axis by convention in this tool. In 3D, the same summation applies across all three axes, and the direction is expressed using direction angles alpha, beta, and gamma relative to the +x, +y, and +z axes.
Problem: Two forces act at a pin: F1 = 200 N at 30 degrees, F2 = 150 N at 120 degrees. Find the resultant.
Step 1. Resolve into components. F1x = 200 cos(30) = 173.2 N, F1y = 200 sin(30) = 100 N. F2x = 150 cos(120) = -75 N, F2y = 150 sin(120) = 129.9 N.
Step 2. Sum components. SumFx = 173.2 - 75 = 98.2 N. SumFy = 100 + 129.9 = 229.9 N.
Step 3. Resultant magnitude: |R| = sqrt(98.2^2 + 229.9^2) = 250.1 N.
Step 4. Resultant direction: theta = atan2(229.9, 98.2) = 66.9 degrees CCW from +x.
| Setup | What you are finding | Notes |
|---|---|---|
| Concurrent coplanar forces | Magnitude and direction of resultant | All forces act at the same point in one plane. 2D mode. |
| 3D concurrent forces | Resultant magnitude and direction angles | Switch to 3D mode. Direction angles given from +x, +y, +z. |
| Equilibrant | Force needed to produce equilibrium | The equilibrant is equal in magnitude to the resultant but opposite in direction. Use flip on any vector. |
| Cable or truss joint | Net force at a joint from multiple member forces | Each member force is a separate vector. Sum gives the external load that joint must carry. |
| Proportional-to-magnitude display | Visual scale of relative force sizes | Enable Prop. to magnitude in the sidebar to scale arrow lengths to force values. |
Angles are measured counterclockwise from the positive x-axis, which is the standard math convention used in most US undergraduate statics textbooks. A force pointing straight up is at 90 degrees; one pointing left is at 180 degrees.
Yes. Toggle the Components switch in the left sidebar. The force cards on the right panel switch to Fx and Fy input fields. Both entry modes drive the same vector internally.
Either enter the angle directly (for example, 180 degrees for a leftward force) or use the Flip button on any force card to reverse its direction without changing the angle entry.
Yes. Switch to 3D mode using the selector in the sidebar. You can draw vectors by dragging from the origin in the current screen plane, then spin the view to see the arrangement in 3D. For precise values, type Fx, Fy, Fz directly in the right panel. The resultant magnitude and direction angles update in real time.
Yes. On phones the controls move to a strip above the canvas and the resultant readout sits in a bar below it, with the full force list one tap away. Drag from the origin to draw vectors, drag a tip to adjust it, and pinch to zoom in 3D mode. The Copy button shows the export image for a long-press save, since mobile browsers restrict direct image clipboard access.