Vector Addition Calculator with Graph

Compute and visualize vector sums with precision and clarity. Enter components or magnitudes with angles; see instant head‑to‑tail diagrams. Compare intermediate steps, resultant magnitude, direction, and component breakdowns. Export tables as tidy CSV for sharing easily. Download neat PDFs with annotated vector graphs today.

Label Input mode Magnitude Angle (°) X Y Color Actions
Results
ΣX0
ΣY0
Resultant magnitude |R|0
Resultant angle θ (°)0

Angles measured from +x axis, counterclockwise. Input angles use selected unit.

Example Data
LabelModeMagnitudeAngleXYColor
AMag+Angle530°4.33012.5Blue
BMag+Angle4120°-23.4641Green
CComponents1-3Red
Formula Used
For each vector \(i\):
Given magnitude \(m_i\) and angle \(\theta_i\):
\(x_i = m_i\cos\theta_i,\quad y_i = m_i\sin\theta_i\)
Given components \(x_i, y_i\):
\(m_i = \sqrt{x_i^2 + y_i^2},\quad \theta_i = \operatorname{atan2}(y_i, x_i)\)
Summation and resultant:
\(\Sigma X = \sum_i x_i,\quad \Sigma Y = \sum_i y_i\)
\(|R| = \sqrt{(\Sigma X)^2 + (\Sigma Y)^2}\)
\(\theta_R = \operatorname{atan2}(\Sigma Y, \Sigma X)\)
How to Use
  1. Choose an input mode per row: components or magnitude+angle.
  2. Select your preferred angle unit from the toolbar.
  3. Pick a color preset for each vector row.
  4. Press Compute to update results and graph.
  5. Toggle head‑to‑tail or origin mode, grid, and labels as needed.
  6. Use Download CSV or Download PDF for exports.
FAQs

Angles are measured in degrees from the positive x‑axis, counterclockwise. Switch the unit selector to radians if needed; calculations adapt instantly and displays update consistently.

Yes. Choose “Radians” in the angle unit selector. Angle inputs, conversions, and the resultant angle will all use radians for display and editing.

No. Color presets only affect the visualization. They help distinguish vectors and improve readability in the graph and exported PDF.

Displayed values are rounded to four decimals for readability. Internal calculations use JavaScript floating‑point precision, suitable for most engineering and classroom uses.

Head‑to‑tail draws each vector starting from the previous head. Origin mode draws all vectors from the origin to compare directions side‑by‑side.

Yes. CSV includes each vector’s color and the current angle unit. The resultant row stores the resultant magnitude plus angle in the chosen unit.

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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.