Torsional Spring
Calculate helical torsion spring torque, angular deflection, spring rate, and bending stress. Free online engineering tool with interactive charts and step-by-step breakdown.
About This Calculator
The Torsional Spring Calculator helps engineers, designers, and students compute the key mechanical properties of helical torsion springs. Enter the spring geometry (wire diameter, coil diameter, active turns), select the material, and specify the applied load to instantly get torque, spring rate, angular deflection, bending stress, and stress correction factors.
Torsion springs work by storing rotational energy when a force is applied to the spring arm, creating torque that twists the coiled wire. The relationship follows the fundamental torsion formula: angular deflection θ = (64 × M × D × Na) / (E × d⁴), where M is torque, D is mean coil diameter, Na is active turns, E is Young's modulus, and d is wire diameter. The spring rate k = M/θ remains constant within the elastic range. Bending stress is calculated with curvature correction factors that account for higher stress on the inner coil surface.
How to Use This Calculator
Start by entering the wire diameter and mean spring coil diameter in millimeters. These define the spring index C = D/d, a critical design parameter typically between 4 and 16. Enter the number of active body turns — this is the number of complete coils that participate in the spring action. Select the spring material from the dropdown; each material has a predefined Young's modulus (E) in GPa. Finally, enter the applied force in newtons and the lever arm length in millimeters — the torque is calculated as M = F × r.
Regional Notes
India (IN): Uses SI units (mm, N, GPa) consistent with IS 7906 standard for spring design. Engineers and students across India use these formulas for mechanical design coursework and industrial applications.
United States (US): While the calculator uses SI units, US engineers commonly work in inches and pounds. Use conversion: 1 mm = 0.03937 in, 1 N = 0.2248 lbf, 1 GPa = 145,038 psi. The formulas and principles are identical regardless of unit system.
United Kingdom (UK): SI units are standard in UK engineering education and industry, following BS EN 13906 for helical torsion spring design. The formulas used align with British and European spring design standards.
Frequently Asked Questions
What is a torsional spring and how does it work?
A torsional spring stores and releases rotational energy by twisting a coiled wire about its axis. When a force is applied to the spring arm at a distance from the center, it creates a torque that causes angular deflection. The spring resists this rotation with a restoring torque proportional to the deflection angle, defined by Hooke's law for torsion: torque = spring rate × angular deflection.
How do I calculate the spring rate of a torsion spring?
The spring rate k of a helical torsion spring is calculated as k = M / θ, where M is the applied torque in N·m and θ is the angular deflection in radians. The torque is computed as M = F × r, where F is the applied force in newtons and r is the lever arm length in meters. The spring rate is constant within the spring's operational range.
What inputs do I need for the torsion spring calculator?
You need six inputs: wire diameter (mm), mean spring coil diameter (mm), number of active turns (dimensionless), material for Young's modulus (steel, aluminum, copper, etc.), applied force (N), and lever arm length (mm). The calculator then computes torque, spring index, angular deflection, spring rate, bending stress, and stress correction factors.
What is the spring index in a torsion spring?
The spring index C is the ratio of the mean coil diameter D to the wire diameter d, given by C = D / d. It is a key design parameter that affects the stress distribution in the spring wire. A typical spring index ranges from 4 to 16. A lower index indicates tighter coiling with higher stress concentration on the inner surface.
How is bending stress calculated in a torsion spring?
Bending stress in a helical torsion spring is calculated as σ = K_i × (32 × M) / (π × d³), where M is the applied torque, d is the wire diameter, and K_i is the inner stress correction factor. The correction factor accounts for curvature effects and is always larger on the inner surface of the coil, making it the critical point for stress analysis.
What materials can I select for the torsion spring calculator?
The calculator supports ten common spring materials: Steel (E = 200 GPa), Aluminum (69 GPa), Copper (110 GPa), Brass (100 GPa), Titanium (110 GPa), Concrete (30 GPa), Wood (10 GPa), Glass (70 GPa), Nylon (3 GPa), and Rubber (0.01 GPa). Select the material that matches your spring to get accurate stiffness and stress calculations.
What is the difference between a torsion spring and a compression spring?
A torsion spring operates by twisting about its axis to store rotational energy, delivering torque when the ends are rotated relative to each other. A compression spring works by being compressed axially, storing linear energy and delivering a pushing force. Torsion springs are used in clothespins, safety pins, and hinges, while compression springs are used in mattresses and valves.
How accurate are the torsion spring calculations?
The calculations use standard engineering formulas from mechanical spring design and are accurate for ideal helical torsion springs within their elastic limit. Results are based on classical bending theory with Wahl-type curvature correction factors. Always verify critical spring designs with physical testing for safety-critical applications.