Cantilever Beam Deflection Calculator

How far will a cantilever tip drop?

This cantilever beam deflection calculator finds how far the free end of an overhanging beam sags under an even load, using deflection = w × L⁴ ÷ (8 × E × I). A 6 ft cantilever carrying 100 lb per foot, with E of 1,600,000 psi and I of 100 in⁴, drops 0.175 inches at the tip. The calculator also shows the L/180 limit for that length, here 0.400 inches, so this beam passes.

Enter the uniform load in lb per foot, the cantilever length in feet, the material’s modulus of elasticity E in psi, and the section’s moment of inertia I in in⁴.

The formula in plain words

The calculator converts feet to inches first:

• w = load per foot ÷ 12, in pounds per inch.
• L = overhang length × 12, in inches.
• Tip deflection = w × L⁴ ÷ (8 × E × I).
• Limit = L ÷ 180.

Length is raised to the fourth power. Add 50% to an overhang and the tip drops about five times as far. Stiffness, E × I, sits underneath the line, so doubling it halves the sag.

Worked examples

1. Default inputs: 100 lb/ft, 6 ft, E = 1,600,000 psi, I = 100 in⁴

• w = 100 ÷ 12 = 8.33 lb/in
• L = 6 × 12 = 72 in
• Deflection = 8.33 × 72⁴ ÷ (8 × 1,600,000 × 100) = 0.175 in
• Limit = 72 ÷ 180 = 0.400 in, so it passes

2. Balcony framing: 150 lb/ft, 4 ft overhang, double 2x10 (I = 197.9 in⁴)

• w = 150 ÷ 12 = 12.5 lb/in
• L = 48 in
• Deflection = 12.5 × 48⁴ ÷ (8 × 1,600,000 × 197.9) = 0.026 in
• Limit = 48 ÷ 180 = 0.267 in, comfortably within

Stretch example 2 to a 6 ft overhang and the tip drops to 0.133 in, five times as much, from only 2 extra feet.

How length drives tip deflection

Load 100 lb/ft, E = 1,600,000 psi, I = 100 in⁴.

Overhang	Tip deflection	L/180 limit	Result
3 ft	0.011 in	0.200 in	Passes
4 ft	0.035 in	0.267 in	Passes
6 ft	0.175 in	0.400 in	Passes
8 ft	0.553 in	0.533 in	Fails
10 ft	1.350 in	0.667 in	Fails
12 ft	2.799 in	0.800 in	Fails

The same beam goes from passing to failing between 6 and 8 ft. That is the fourth-power effect.

Where cantilevers show up

Example	What is cantilevered	Usual concern
Deck joist overhang	Joists past the drop beam	Bounce at the edge, uplift at the back
Deck beam overhang	Beam past the last post	Point loads from the joists above
Balcony	Joists or steel beams from the wall	Connection at the wall, drainage
Roof overhang	Rafter tails past the wall	Snow and wind uplift
Shelf or bracket	The bracket arm	Long-term creep in wood

How to gather the inputs

• Length: measure from the face of the support to the free tip, in feet.
• Load per foot: multiply the area load in psf by the width the member carries. A joist 16 in on center (1.33 ft) under 50 psf carries 50 × 1.33 = 66.7 lb/ft.
• E and I: use the published design value for your lumber grade, and width × depth³ ÷ 12 for I. The moment of inertia calculator handles other shapes.

Common mistakes

• Ignoring the back-span. A cantilever needs enough beam behind the support to stop it tipping. Deflection alone does not check that.
• Point loads at the tip. A planter or hot tub at the edge is a point load, which this uniform-load formula does not cover.
• Using simple-span results. A supported beam answer will understate cantilever sag about tenfold. For two-support beams, use the beam deflection calculator.
• Nominal lumber sizes. Use actual depth when computing I.

To size the joists themselves, see the deck joist calculator.

This is a planning estimate for stiffness only. Cantilevered decks and balconies carry people above the ground. Have a licensed structural engineer or your building department confirm the design.