| Scenario | Inputs | Outputs (approx.) |
|---|---|---|
| Components (upward) | Tx = 120, Ty = 90 | T ≈ 150, θ ≈ 36.87° above horizontal |
| Components (downward) | Tx = 200, Ty = −60 | T ≈ 208.81, θ ≈ 343.30° (−16.70°) |
| Components (left + up) | Tx = −100, Ty = 100 | T ≈ 141.42, θ ≈ 135.00° from +X |
| Resultant + Tx | T = 500, Tx = 300, Ty upward | Ty ≈ 400, θ ≈ 53.13° above horizontal |
| Resultant + Ty | T = 800, Ty = 600, Tx right | Tx ≈ 529.15, θ ≈ 48.59° above horizontal |
| Magnitude + angle | T = 200, θ = 30° from horizontal | Tx ≈ 173.21, Ty ≈ 100.00 |
| Magnitude + vertical reference | T = 300, θ = 20° from vertical | Tx ≈ 102.61, Ty ≈ 281.91 |
| Two-cable support (find angle) | W = 500, n = 2, T limit = 350 | θ ≈ 45.58° from horizontal (minimum) |
| Three-cable support (find tension) | W = 900, n = 3, θ = 40° | T per cable ≈ 467.09 (from horizontal) |
- T = √(Tx² + Ty²) — resultant magnitude from components.
- θ = atan2(Ty, Tx) — signed angle from +horizontal axis.
- Tx = T·cos(θ) and Ty = T·sin(θ) — components from magnitude and angle.
- W = n·T·sin(θ) — symmetric supported load, θ from horizontal.
- θ = asin(W/(n·T)) — required angle for a tension limit.
- Select the mode that matches your known values.
- Pick a unit label so outputs stay consistent.
- Enter the numbers, including sign and direction choices.
- Click Calculate to view angles and components.
- Use Download CSV or Download PDF for records.
1) What a tension angle means
A tension angle describes the direction of a pulling force relative to a chosen axis. In many layouts, the reference is the horizontal line (+Tx). As the angle rises, the vertical share increases and the horizontal share decreases. This tool also shows a 0–360° direction from +X.
2) Reading component inputs with signs
Component mode uses Tx and Ty. Positive Tx pulls right, negative pulls left. Positive Ty is upward, negative is downward. Example: Tx = 200 and Ty = −60 gives magnitude ≈ 208.81 with an angle near −16.70°. If both components are zero, no direction exists, so the calculator blocks the result.
3) Resultant magnitude from components
The magnitude comes from T = √(Tx² + Ty²). If Tx = 120 and Ty = 90, T becomes 150. This is useful when you measure horizontal and vertical effects but need one tension value for logs or comparisons.
4) Angle calculation and correct quadrant
Angles are computed with atan2(Ty, Tx), which places the direction in the correct quadrant. If Tx is negative and Ty is positive (Tx = −100, Ty = 100), the direction is 135° from +X, not 45°. That matters for anchors, pulleys, and alignment. The calculator also shows acute angles from horizontal and vertical for quick reading.
5) Converting between horizontal and vertical references
Some drawings specify the angle from the vertical. For acute cases: angle from vertical = 90° − angle from horizontal. With T = 300 and 20° from vertical, the horizontal reference is 70°, producing Tx ≈ 102.61 and Ty ≈ 281.91. If you enter an angle from vertical, the calculator converts it internally before computing components.
6) Supported load with equal cables
In supported-load mode, equal cables share the vertical requirement. The simplified balance is W = n·T·sin(θ), where θ is from horizontal. With W = 500, n = 2, and T = 350, the minimum θ is ≈ 45.58°. Increasing θ lowers the needed tension per cable, while shallow angles can drive tension high. This mode assumes symmetric geometry and equal sharing.
7) Rounding, units, and quick verification
Use a unit label that matches your inputs, such as N, lbf, or kgf, and keep it consistent across load and tension. Rounding should match measurement precision; 2–4 decimals is often enough. A quick check is Tx/T and Ty/T staying between −1 and +1. Compare your result to the example table, then export CSV or PDF for records.
Use the reference your drawing or standard uses. Many mechanics problems use horizontal. Many rigging sketches use vertical. This page displays both so you can copy the one your documentation expects.
0–360° is a compass-style direction from +X. The signed angle shows above or below the horizontal baseline. Both describe the same direction, just in different formats.
Enter negative Tx for left and negative Ty for downward, or choose the direction options in the “resultant + one component” mode. The calculator uses atan2, so the quadrant stays correct.
Avoid mixing. Keep load and tension in the same unit system, then label the unit once. If you must convert, convert all inputs first so the output remains consistent.
Because the vertical component is T·sin(θ). When θ is small, sin(θ) is small, so each cable must carry much more tension to provide the same vertical support.
No. Use it for geometry and quick checks, then apply proper safety factors, dynamic effects, hardware ratings, and applicable standards. When in doubt, consult a qualified engineer or rigger.