Equilibrium of Forces Calculator to Solve Static...
Calculate whether a system of forces is in equilibrium. Find unknown forces and torques so that the net force and net torque equal zero.
What is Equilibrium of Forces?
A system is in static equilibrium when the net force and net torque acting on it equal zero. This is the foundation of structural engineering — every bridge, building, and machine must satisfy equilibrium conditions to remain stable.
⚖️ Equilibrium of Forces Calculator
Use our free calculator for instant, accurate results.
📐 Formula
ΣF = 0 and Στ = 0
ΣFx = 0, ΣFy = 0, ΣFz = 0 (translational). Στ = Σ(F × d) = 0 (rotational, about any pivot).
📝 Worked Example
A 10 kg sign hangs from two ropes at 30° and 60° from horizontal:
Resolve vertically and horizontally to find tension in each rope using the equilibrium equations.
T₁cos30 + T₂cos60 = mg → T₁=49N, T₂=85N (approx)
📝 How to Use the Calculator
❓ FAQ
What is the first condition of equilibrium?
ΣF = 0 — the vector sum of all forces is zero (no translational acceleration).
What is the second condition?
Στ = 0 — the sum of all torques about any point is zero (no rotational acceleration).
Veer Kumavat
Founder & AuthorVeer is a 14-year-old student from Nashik, Maharashtra, who built SciFi Calculators to help students worldwide master STEM subjects. He is passionate about making complex science and math problems accessible through intuitive digital tools.