Leaf Spring Calculator

Estimate fixed-end bending stress, tip deflection, slope, and stiffness for a rectangular cantilever leaf spring under a transverse end load.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Geometry, material, and load

Use one straight constant-section cantilever with the load applied at its free end.

Beam response

Maximum bending stress750.00 MPaExtreme-fibre magnitude at the fixed end.

Tip deflection, δ29.76 mm

Stiffness, k33.60 N/m

Bending moment, M_x50.00 N·mm

Second moment, I_x0.0067 mm⁴

Section modulus, S_x0.0667 mm³

Tip slope, θ0.89 rad

If deflection is not small relative to L, use a geometrically nonlinear model instead of these values.

How to use

Confirm the leaf is one straight, constant rectangular cantilever with an ideal clamp and a transverse free-end point load; there is one calculation mode.
Enter width b, thickness h, and free length L in mm, and Young’s modulus E in GPa.
Enter positive tip-load magnitude F in N. Reverse loading has equal magnitudes but opposite physical direction.
Select Calculate, or edit a valid input, to update every result.
Select Reset example to restore b = 10 mm, h = 0.2 mm, L = 50 mm, E = 210 GPa, and F = 1 N.
Interpret σ_max as a fixed-end stress screen, δ and θ as small-deflection response, and k as equivalent end stiffness. Correct any warning before use.
Do not use this model for large deflection, non-rectangular or tapered leaves, distributed/intermediate loads, uncertain clamps, short shear-sensitive beams, fatigue, buckling, or safety qualification.

Worked example

For b = 10 mm, h = 0.2 mm, L = 50 mm, E = 210 GPa, and F = 1 N, the result is M_x = 50.00 N·mm, I_x = 0.0067 mm⁴, S_x = 0.0667 mm³, σ_max = 750.00 MPa, δ = 29.76 mm, θ = 0.89 rad, and k = 33.60 N/m. The very large δ/L ratio means this case demonstrates the equations and rounding but is outside small-deflection applicability for final design.

Equations used

b_m = b × 10⁻³, h_m = h × 10⁻³, L_m = L × 10⁻³, E_Pa = E × 10⁹

M_x = F L_m

I_x = b_m h_m³ / 12

S_x = I_x / (h_m/2) = b_m h_m² / 6

σ_max = M_x / S_x

δ = F L_m³ / (3 E_Pa I_x)

θ = F L_m² / (2 E_Pa I_x)

k = F / δ = 3 E_Pa I_x / L_m³

Here b_m, h_m, and L_m are metres; E_Pa is Pa; F is N; M_x is N·m before display conversion; I_x is m⁴; S_x is m³; σ_max is Pa; δ is m; θ is rad; and k is N/m.

Theory and method

A cantilever beam is the basis of many leaf springs. This model applies Euler–Bernoulli bending to a straight prismatic rectangular leaf with an ideal fixed support and a transverse point load at the free end. It assumes homogeneous isotropic linear elasticity, plane sections remaining plane, and small displacement and rotation.

It excludes shear deformation, geometric nonlinearity, clamp compliance, fatigue, buckling, contact, residual stress, manufacturing tolerances, and safety factors. Independently establish allowable stress and duty-cycle criteria. Reference: Anton van Beek, Advanced Engineering Design, cantilever leaf-spring equations (Tables 14.3–14.5), and standard Euler–Bernoulli beam theory.

Continue in TriboSolver for geometry refinement and independent structural analysis. Related: Cross-Spring Flexure Hinge Calculator.