Structural Engineering
Beam Deflection Calculator
📐 δ = PL³ / (3EI)
Calculate beam deflection for various beam types and loading conditions.
Beam Configuration
Beam Type
Cantilever: fixed at one end | Simply Supported: pinned at both ends | Fixed-Fixed: fixed at both ends
Loading Type
Point load at end (cantilever) or center (simply supported/fixed)
Beam Properties
Length (L)
mm
Beam length in millimeters
Load (F / w)
N
Force (N) or uniform load (N/mm) depending on loading type
Modulus of Elasticity (E)
N/mm²
Young's modulus (Steel: 200,000 N/mm²)
Moment of Inertia (I)
mm⁴
Second moment of area (I) in mm⁴
Cantilever · Point Load
Deflection
0mm
Max Deflection
0 mm
δ = PL³ / (3EI)
Beam Type
Cantilever
Loading Type
Point Load
Stiffness (EI)
0 N·mm²
Deflection Ratio
1 / 0
📊 Detailed Breakdown
| Parameter | Value | Unit |
|---|
How the formula works
Cantilever Point Load: δ = PL³ / (3EI)
- Cantilever · Point Load: δ = PL³ / (3EI)
- Cantilever · Uniform Load: δ = wL⁴ / (8EI)
- Simply Supported · Point Load (center): δ = PL³ / (48EI)
- Simply Supported · Uniform Load: δ = 5wL⁴ / (384EI)
- Fixed-Fixed · Point Load (center): δ = PL³ / (192EI)
- Fixed-Fixed · Uniform Load: δ = wL⁴ / (384EI)
- Stiffness (EI) = Modulus × Moment of Inertia
- Deflection Ratio = L / δ (span-to-deflection ratio)
- Ensure consistent units (N, mm, N/mm², mm⁴)