Combine up to four vectors and view components. See direction, magnitude, and step explanations instantly. Export clean results for homework, labs, and presentations easily.
| Scenario | Vector A | Vector B | Vector C | Expected R | Expected θ |
|---|---|---|---|---|---|
| Two forces | 10 @ 0° | 10 @ 90° | — | 14.142 | 45.000° |
| Three displacements | 12 @ 30° | 8 @ 210° | 5 @ 90° | 9.539 | 79.107° |
| Component inputs | (6, 2) | (-1, 5) | (3, -4) | 8.062 | 21.801° |
This calculator supports up to four vectors for common force, velocity, and displacement tasks. Typical datasets include magnitudes from 5–5000 units, angles from the positive x‑axis, and signed component readings from instruments. Keep units consistent across vectors. In polar mode, enter magnitude and angle. In component mode, enter x and y values. The tool sums components first, then derives the final magnitude and direction. For physics classes, use degrees; for navigation, treat x as east and y as north, then interpret direction accordingly in your notes each.
The component method is highly auditable. Each vector becomes x and y parts, then totals are computed as Σx and Σy. This mirrors engineering notebooks and makes reviews easier. If you already have east and north readings, components avoid conversion mistakes. The output shows summed components and the derived angle using atan2, which handles all quadrants and negative values correctly.
Polar inputs reduce entry to magnitude and angle per vector. Internally, the calculator converts to components with cosine and sine, so the math stays consistent. Minor rounding differences can appear near 90° or 270°, where one component should approach zero. Use the rounding control to match your reporting standard, such as 2 decimals for homework or 4 decimals for lab data. Confirm the angle reference before comparing results.
The resultant magnitude is the single equivalent vector replacing all inputs. Direction is reported in degrees from 0–360°, measured counterclockwise from the positive x‑axis. A magnitude near zero indicates near-cancellation; small measurement error can then swing direction sharply. Review Σx and Σy to understand cancellation. The calculator also provides a unit direction vector (Rx/R, Ry/R) for projections and dot‑product work.
The CSV export captures inputs, computed components, totals, and the final resultant for archiving or sharing. The PDF export creates a compact summary for attachments and submissions. Validation rejects negative magnitudes in polar mode and highlights missing fields. Keep vector count aligned with your scenario and disable unused rows. Recalculate after edits so exports stay synchronized with the displayed results.
Angles are measured from the positive x-axis, increasing counterclockwise. This matches standard trigonometry and most physics diagrams. If your problem uses bearings, convert them before entry.
When vectors nearly cancel, Σx and Σy approach zero. Tiny measurement or rounding differences can move the atan2 angle significantly. In such cases, focus on the components and uncertainty bounds, not just the angle.
Not in a single calculation. Choose one mode for consistency. If you have mixed data, convert your polar values to components (or vice versa) first, then enter all vectors using the same mode.
Use a rounding level that matches your instrument precision and reporting rules. Two decimals is common for classroom work, while three to four decimals fits many lab datasets. Keep the same rounding for exports and tables.
It is the normalized direction of the resultant: (Rx/R, Ry/R). It has length 1 and keeps only direction information. Use it for projections, scaling, or combining the direction with a new magnitude.
Exports include your vector inputs, computed components, totals (Σx, Σy), resultant magnitude R, direction θ, and unit direction. CSV is best for spreadsheets, while PDF is convenient for attachments and submissions.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.