# Beam Deflection Calculator Look up and compute the maximum deflection for four classic beam cases: cantilever with end point load (δ=PL³/3EI), cantilever with UDL (δ=qL⁴/8EI), simply supported with mid-span point load (δ=PL³/48EI), and simply supported with UDL (δ=5qL⁴/384EI). > Canonical page: https://elysiatools.com/en/tools/deflection-calculator - **Category:** Math & Numbers - **Keywords:** beam deflection, deflection, bending, PL³/3EI, qL⁴/8EI, PL³/48EI, 5qL⁴/384EI, cantilever, simply supported, strength of materials, mechanics of materials, civil engineering ## Overview The Beam Deflection Calculator computes the maximum deflection for four classic structural beam configurations: cantilever beams with end point loads or uniformly distributed loads (UDL), and simply supported beams with mid-span point loads or UDLs. By inputting the span length, load magnitude, Young's modulus, and the second moment of area, engineers and students can instantly determine structural deflection using standard mechanics of materials formulas. ## Inputs - **Support & Load Case** (select) - **Point Load P (N)** (number): Required for point-load cases. - **Uniformly Distributed Load q (N/mm)** (number): Required for UDL cases. - **Span Length L (mm)** (number): e.g. 4000 - **Young's Modulus E (MPa)** (number): Modulus of elasticity in MPa (= N/mm²). Steel ≈ 210000, aluminum ≈ 70000. - **Second Moment of Area I (mm⁴)** (number): Area moment of inertia of the cross-section about the bending axis, in mm⁴. - **Decimal Places** (number) ## When to use - When designing structural steel or aluminum beams and verifying that maximum deflection stays within allowable building code limits. - When analyzing cantilever or simply supported beam setups under point loads or uniformly distributed loads (UDL) during mechanical design. - When solving mechanics of materials homework problems or verifying manual beam bending calculations. ## How it works - Select the support and loading case, such as a cantilever or simply supported beam with either a point load or a uniformly distributed load. - Enter the physical properties of the beam, including the span length (L), Young's Modulus (E), and the second moment of area (I). - Input the load value, using either point load (P) in Newtons or uniformly distributed load (q) in Newtons per millimeter. - Click calculate to evaluate the deflection using the corresponding analytical formula (e.g., PL³/3EI or 5qL⁴/384EI) and view the maximum deflection value. ## Use cases - Verifying structural compliance of a steel I-beam supporting a uniform floor load. - Calculating the tip deflection of an aluminum cantilever bracket holding a sensor payload. - Comparing deflection differences between point loads and distributed loads on a wooden joist. ## Frequently asked questions ### What units should I use for the inputs? Use Newtons (N) for point loads, Newtons per millimeter (N/mm) for UDLs, millimeters (mm) for span length, Megapascals (MPa or N/mm²) for Young's Modulus, and mm⁴ for the second moment of area. ### Which beam configurations are supported? The calculator supports cantilever beams with end point loads or UDLs, and simply supported beams with mid-span point loads or UDLs. ### How do I find the second moment of area (I) for my beam? You can look up the second moment of area (I) in standard steel section tables for standard profiles, or calculate it using geometric formulas for simple shapes like rectangles (bh³/12). ### What formula is used for a simply supported beam under a UDL? The calculator uses the classic formula: δ = 5qL⁴ / (384EI) to find the maximum deflection at the mid-span. ### Can I adjust the precision of the calculated deflection? 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