Formula Used
The calculator uses the component method. Each vector is split into x and y parts.
Ax = A cos θA
Ay = A sin θA
Bx = B cos θB
By = B sin θB
Rx = Ax + Bx
Ry = Ay + By
R = √(Rx2 + Ry2)
θR = atan2(Ry, Rx)
The cosine check is R = √(A² + B² + 2AB cos φ), where φ is the included angle.
How to Use This Calculator
- Enter a name for the electrical quantity, such as voltage phasor or magnetic field.
- Enter the shared unit, such as V, A, N, or T.
- Add the magnitude and angle for vector A.
- Add the magnitude and angle for vector B.
- Select degrees or radians for the angle inputs.
- Choose decimal places for the final display.
- Press the calculate button to view the resultant above the form.
- Use CSV or PDF buttons to download the same result.
Example Data Table
| Example | Vector A | Angle A | Vector B | Angle B | Expected Use |
|---|---|---|---|---|---|
| Voltage phasors | 12 V | 30° | 8 V | 140° | Find combined AC voltage effect. |
| Current phasors | 15 A | 0° | 10 A | 60° | Estimate total current direction. |
| Magnetic fields | 0.40 T | 25° | 0.25 T | 120° | Combine field components. |
| Conductor forces | 18 N | 210° | 22 N | 315° | Check net mechanical effect. |
Resultant of Two Concurrent Vectors in Electrical Work
Why This Calculator Matters
Concurrent vectors meet at one point. In electrical work, they describe alternating quantities, phasors, forces on conductors, or field components. A quick resultant compares influences without drawing a scale diagram. The calculator converts each vector into horizontal and vertical components. It then adds matching components and rebuilds the final vector.
Electrical Meaning
Many electrical values have both size and direction. Current, voltage phasors, magnetic field strength, and impedance quantities can be represented by vectors. When two vectors act at the same point, their combined effect is not found by ordinary addition unless their directions match. The angle between them changes the answer. A small angle usually gives a larger resultant. An opposite angle can cancel part of the effect.
What The Results Show
The magnitude is the strength of the combined vector. The direction angle shows where the resultant points from the chosen reference axis. The x and y components show how much of the result acts along each axis. The angle between vectors helps check the cosine formula. The equilibrium vector is useful. It is equal in size to the resultant, but points opposite.
Practical Use Cases
Use this tool when checking two phasors in an AC circuit. It helps with two magnetic fields crossing at one point. Students can verify vector diagrams before submitting homework. Technicians can estimate effects before choosing instruments or settings. Engineers can compare component sums with a graphical answer.
Accuracy Tips
Use the same unit for both magnitudes. Do not mix volts with amps or newtons. Choose degrees unless your source gives radians. Keep the reference direction consistent. Positive angles are measured counterclockwise. Negative angles can represent clockwise rotation. Increase decimal places when vectors nearly cancel.
Reading The Output
A positive x component points along the reference axis. A negative x component points opposite it. A positive y component points above the axis. A negative y component points below it. The final angle uses all four quadrants. That makes the answer safer than using a simple tangent ratio alone.
Final Notes
Vector addition is a core skill. This calculator keeps the steps visible. It supports learning, checking, and documentation. Downloadable records help store results for reports, labs, and maintenance notes.
FAQs
What are concurrent vectors?
Concurrent vectors are vectors that act through the same point. Their tails or lines of action meet at one location, so they can be added as a single resultant effect.
Can I use this for AC phasors?
Yes. Enter phasor magnitudes and phase angles using the same unit. The calculator returns the combined magnitude, direction, and rectangular components.
Should I use degrees or radians?
Use the unit your source data uses. Most electrical phasor diagrams use degrees, while some engineering formulas and software outputs use radians.
Why does the calculator use atan2?
atan2 checks both x and y component signs. This gives the correct quadrant and avoids direction errors caused by a simple tangent ratio.
What does the equilibrium vector mean?
The equilibrium vector has the same magnitude as the resultant but points in the opposite direction. It balances the two input vectors at the same point.
Can the resultant be zero?
Yes. If two vectors have equal magnitudes and opposite directions, their x and y components can cancel. The final direction then has no unique value.
Why is the cosine check included?
The cosine formula gives a second way to verify the magnitude. It uses both magnitudes and the included angle between the two vectors.
Can I download my result?
Yes. Use the CSV button for spreadsheet records. Use the PDF button for a simple printable report containing inputs, formulas, and results.