Beam Deflection Calculator
Beam Deflection is evaluated from Load Configuration, Point Load and Distributed Load. The calculation reports Maximum Deflection, Maximum Deflection and L/δ Ratio.
Results
About the Beam Deflection Calculator
The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.
Formula basis:
Simply supported center load: δ = PL^3 / (48EI)
Simply supported uniform load: δ = 5wL⁴ / (384EI) [w in lb/in]
Cantilever end load: δ = PL^3 / (3EI)
Cantilever uniform load: δ = wL⁴ / (8EI) [w in lb/in]
All inputs in US customary: L in inches, P in lb, w in lb/in, E in psi, I in in⁴ → δ in inches
Code check: δ must be <= L/360 for floor live load (per IBC 2021)
Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.
Formula & How It Works
The calculation applies the following relations exactly as recorded in the metadata: Simply supported center load: δ = PL^3 / (48EI) Simply supported uniform load: δ = 5wL⁴ / (384EI) [w in lb/in] Cantilever end load: δ = PL^3 / (3EI) Cantilever uniform load: δ = wL⁴ / (8EI) [w in lb/in] All inputs in US customary: L in inches, P in lb, w in lb/in, E in psi, I in in⁴ → δ in inches Code check: δ must be <= L/360 for floor live load (per IBC 2021) Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.
Worked Examples
Example 1: Floor Joist — Uniform Load Check
Inputs
With Load Configuration = Simply supported - uniform load, Distributed Load = 50, Beam Span = 16 and Elastic Modulus = 1,600 as the stated inputs, the result is Maximum Deflection = 0.5236 in, Maximum Deflection = 13.3 mm and L/δ Ratio = 367. Each value corresponds to the declared output fields.
Example 2: Steel Beam — Center Point Load
Inputs
With Load Configuration = Simply supported - center point load, Point Load = 20,000, Beam Span = 24 and Elastic Modulus = 29,000 as the stated inputs, the result is Maximum Deflection = 0.6439 in, Maximum Deflection = 16.356 mm and L/δ Ratio = 447. Each value corresponds to the declared output fields.
Example 3: Cantilever Deck — End Load
Inputs
With Load Configuration = Cantilever - end point load, Point Load = 1,500, Beam Span = 8 and Elastic Modulus = 1,600 as the stated inputs, the result is Maximum Deflection = 0.363 in, Maximum Deflection = 9.221 mm and L/δ Ratio = 264. Each value corresponds to the declared output fields.
Example 4: Aluminum Diving Board — Cantilever Uniform Load
Inputs
With Load Configuration = Cantilever - uniform load, Distributed Load = 30, Beam Span = 10 and Elastic Modulus = 10,000 as the stated inputs, the result is Maximum Deflection = 0.0563 in, Maximum Deflection = 1.429 mm and L/δ Ratio = 2,133. Each value corresponds to the declared output fields.
Common Use Cases
- Calculate maximum deflection of a floor joist under uniform load
- Find center deflection of a simply supported beam with point load
- Check if beam deflection meets L/360 code requirements