What is the formula for UDL deflection?

For a simply supported beam with a full-span uniform distributed load w and span L, the maximum mid-span deflection is δ = 5wL⁴ / (384EI). This is the standard elastic beam formula derived from the Euler-Bernoulli beam equation.

What is the formula for a center point load?

For a simply supported beam with a concentrated load P at mid-span, the maximum deflection at center is δ = PL³ / (48EI). The deflection is largest at the point of load application, which coincides with mid-span.

What is an acceptable deflection limit?

Most building codes limit live-load deflection to L/360 for floor beams (to prevent cracking of brittle finishes) and L/240 for roof beams or combined dead+live loads. Compare your calculated δ to these limits: if L/δ ≥ 360, you meet the L/360 limit.

What units should I use for E and I?

In Imperial mode, enter E in ksi (kips per square inch) and I in in⁴. Common values: steel A992 E = 29,000 ksi; Douglas Fir No. 2 E ≈ 1,600 ksi. In Metric mode, enter E in GPa and I in cm⁴. Steel E = 200 GPa; concrete E ≈ 25–30 GPa.

Does this handle cantilevers or continuous beams?

No. This calculator covers only simply supported beams (pinned at both ends) with either a full-span UDL or a single concentrated load at mid-span. Cantilevers, partial loads, and continuous beams require different formulas or dedicated software.

Why does my deflection seem very large?

Large deflections often indicate a unit mismatch. Confirm that E and I are in the correct units for the selected system. For example, entering E in psi instead of ksi (without dividing by 1,000) will produce deflections 1,000 times too large.

Beam Deflection Calculator

Calculate maximum deflection of a simply supported beam under a uniform distributed load or a point load at center.

Beam Parameters

Load Type

Span Length (L) — ft

Uniform Load (w) — kips/ft

Modulus of Elasticity (E) — ksi

Steel ≈ 29,000 ksi | Wood ≈ 1,600 ksi

Moment of Inertia (I) — in⁴

See beam section tables for I values.

Results

Enter beam parameters and click Calculate.

Beam Diagram

Summary

This free online beam deflection calculator computes the maximum mid-span deflection of a simply supported beam for two common load cases: a uniform distributed load (UDL) across the full span and a concentrated point load at the center. Enter the span length, load, modulus of elasticity, and moment of inertia to get instant results in Imperial or Metric units. Results include the deflection value, the span-to-deflection ratio, and a serviceability check against common code limits.

How it works

Select your unit system: Imperial (kips, ft, in) or Metric (kN, m, cm).
Choose the load type: Uniform Distributed Load (UDL) or Point Load at Center.
Enter the beam span length between supports.
Enter the load magnitude (UDL in force per length, or point load in force units).
Enter the modulus of elasticity (E) for your beam material.
Enter the moment of inertia (I) of the beam cross-section.
Click Calculate to see the maximum deflection and serviceability ratio.

Use cases

Checking floor joist deflection against L/360 live-load serviceability limits.
Sizing steel beams carrying a concentrated load from a column above.
Verifying that wood beams meet L/240 total-load deflection limits.
Quick hand-check of structural software output before detailed analysis.
Comparing deflection of steel vs. wood vs. concrete sections by swapping E and I.
Educational reference for structural engineering and construction students.
Pre-screening beam depth before running a full finite-element model.
Estimating roof beam deflection under snow or equipment point loads.

Frequently Asked Questions

Last updated: 2026-05-25 · Reviewed by Nham Vu