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Truss Method of Joints Calculator

Enter the applied vertical load and the member angle to solve the joint by the method of joints.

How it is calculated

The tool solves one joint where a vertical load is carried by a single inclined member. Balancing the vertical forces at the pin gives the member's axial force from the angle θ it makes with the horizontal, in degrees:

F = load ÷ sin θ
horizontal component = F × cos θ

The force and its horizontal part are shown as positive magnitudes in newtons, to one decimal. The angle must be above 0° and below 180°; otherwise there is no result. The note depends only on the sign of the load you enter: a positive load is reported as compression, a negative load as tension, and a load of zero as "Zero force". The tool has no idea what the rest of the truss does. Bigger loads and flatter angles give larger forces, since sin θ shrinks toward zero.

Worked example

A 10,000 N vertical load acts on a joint held by one member at 30° to the horizontal. sin 30° = 0.5, so the member force is 10,000 ÷ 0.5 = 20,000.0 N. The horizontal component is 20,000 × cos 30° = 20,000 × 0.866 = 17,320.5 N, and because the load is positive the tool notes compression. The member carries twice the load, which is why shallow members in a roof truss work harder than steep ones.

Try this example →

Common mistakes

  • Measuring the angle from the vertical. The formula uses the angle from the horizontal; typing 60 for a member 30° off the horizontal gives 11,547.0 N instead of 20,000.0 N.
  • Using kilonewtons or kilograms. The load is read as newtons and the result is in newtons; a mass in kg must first be multiplied by about 9.81.
  • Applying the single-joint result to a joint with two or more unknown members. The tool assumes one inclined member takes the whole vertical load, so it cannot solve a typical interior joint.
  • Trusting the Compression or Tension label as a physical finding. It only follows the sign you typed for the load, so a joint that really puts the member in tension needs a negative load to get that label.
  • Entering very small angles. At 1° the member force is over 57 times the load (572,986.9 N for 10,000 N), which is correct maths but a sign the geometry is unrealistic.

About this calculator

The method of joints is the standard hand-calculation technique for solving statically determinate trusses in structural and civil engineering: at each pin joint, the truss members are treated as two-force members (axial tension or compression only), and equilibrium requires the sum of forces in both the horizontal and vertical directions to equal zero — ΣFx = 0 and ΣFy = 0. At a simple joint with one unknown member inclined at angle θ carrying a vertical applied load, the member force works out to load ÷ sin(θ), with its horizontal pull or push on the joint equal to that force times cos(θ).

Engineers walk through a truss joint by joint, starting where only two unknown member forces meet so the two equilibrium equations can be solved directly, then move to the next joint using the forces just found. This calculator reproduces that single-joint case — enter the applied vertical load and the member angle to get the axial member force and its horizontal component, the same numbers a bridge or roof-truss design check would start from.

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