Example Data Table
| Vector |
Mode |
Magnitude |
Angle |
Fx |
Fy |
| F1 |
magnitude-angle |
120 N |
30° |
103.923 N |
60.000 N |
| F2 |
magnitude-angle |
95 N |
145° |
-77.819 N |
54.490 N |
| F3 |
components |
80.777 N |
291.801° |
30.000 N |
-75.000 N |
| Answer |
resultant |
68.618 N |
35.135° |
56.104 N |
39.490 N |
Formula Used
Horizontal component: Fx = F cos(θ)
Vertical component: Fy = F sin(θ)
Total components: ΣFx = Fx1 + Fx2 + ... and ΣFy = Fy1 + Fy2 + ...
Resultant force: R = √((ΣFx)² + (ΣFy)²)
Direction: θ = atan2(ΣFy, ΣFx)
Equilibrant: same magnitude as R, but 180 degrees opposite.
Acceleration check: a = R / m, after converting force to newtons.
How to Use This Calculator
Choose the force unit and angle unit first. Select the direction convention used by your worksheet.
Enter each force by magnitude and angle, or switch the row to component mode. Blank vectors are ignored.
Add mass only when the problem asks for acceleration. Enter an expected answer when you want an answer key comparison.
Press Calculate to show the result above the form. Use the export buttons to save the answer key.
About the Force Vector Answer Key
This tool supports lesson 2.1.4 style practice on force vectors. It turns each force into horizontal and vertical components. Then it adds every component to build a clear answer key. You can enter forces by magnitude and angle. You can also enter known x and y components. This helps when a diagram already gives component values.
Why Components Matter
Force vectors need direction as well as size. A pull of 20 N east is not the same as 20 N north. The calculator keeps that direction by using signs. Positive x points right. Negative x points left. Positive y points up. Negative y points down. Angles are measured from the positive x axis, unless you choose the clockwise option.
Reading the Answer Key
The output shows each resolved vector. It lists Fx, Fy, magnitude, and direction. It also shows the resultant force. The resultant is the single force that matches the combined effect of all entered forces. If the resultant is near zero, the forces are balanced. If it is not zero, an object may accelerate in the resultant direction.
Classroom Use
This page is useful for answer keys because it shows the same method used in class. Students can compare their component table with the calculated table. Teachers can export the final data for checking, printing, or grading. The expected answer box also helps compare a supplied answer with the calculated resultant.
Best Practice
For best results, draw the axes first. Mark right and up as positive. Enter each angle carefully. Use degrees for most classroom problems. Use radians only when the source problem gives radians. Keep units consistent for all forces. Do not mix newtons and pounds in one run unless the values were converted before entry.
Advanced Checks
The mass field is optional. When mass is entered, the tool estimates acceleration from Newton's second law. This adds one more check for dynamics problems. The tolerance field controls the equilibrium message. A small tolerance is strict. A larger tolerance allows rounding differences. Use the decimal control to match your worksheet precision. Always review signs before copying the final answer.
It also supports multi-force diagrams with repeated rows. This makes pulley, ramp, tension, thrust, and load examples easier to audit during physics review sessions. This supports final worksheet submission.
FAQs
1. What does this force vector calculator find?
It finds x components, y components, resultant force, resultant direction, equilibrant force, and optional acceleration. It also compares your expected answer with the calculated answer.
2. Can I enter only x and y components?
Yes. Choose component mode for that vector. The calculator will compute its magnitude and direction from Fx and Fy.
3. Which angle direction should I use?
Use the same convention as your worksheet. Most physics problems measure counterclockwise from the positive x axis.
4. What does the equilibrant mean?
The equilibrant is the force that would balance the resultant. It has the same magnitude, but points in the opposite direction.
5. Why is my answer not balanced?
The net force is larger than your tolerance. Check signs, angles, units, and rounded values. A small input error can change equilibrium.
6. Can I use pounds of force?
Yes. Select pound-force as the unit. Use the same unit for all entries so the resultant stays consistent.
7. How is acceleration calculated?
Acceleration is calculated from net force divided by mass. The force is converted to newtons before using kilograms.
8. What exports are available?
You can download a CSV table for spreadsheets. You can also download a simple PDF answer key for printing or sharing.