Cantilever Beam Calculator

Analyze cantilevered beams with point loads, uniform loads, and combined loading conditions.

Point Load at Free End

M_max = PL (at fixed end)
V_max = P | δ_max = PL³/3EI (at free end)

Point Load (P)

Load Unit

Cantilever Length (L)

Length Unit

E (psi)

I (in⁴) - for deflection

Results

Max Moment (at fixed end)

—

Reaction at Support (R) —

Fixed End Moment —

Max Shear (V) —

Max Deflection (at tip) —

Deflection Ratio (L/δ) —

Slope at Tip (θ) —

Important: Cantilevers deflect significantly more than simply supported beams. Typical limit is L/180 for cantilevers.

Point Load at Distance 'a'

M_max = Pa (at fixed end)
δ_tip = Pa²(3L-a)/6EI

Point Load (P) - lbs

Total Length (L) - ft

Load Position (a) - ft from fixed end

E (psi)

I (in⁴)

Results

Max Moment (at fixed end)

—

Reaction (R) —

Fixed End Moment —

Deflection at Load —

Deflection at Tip —

Moment at Load Location —

Note: Beyond the load point, the beam has no moment or shear - only deflection from the rotation at the load point.

Uniform Load on Cantilever

M_max = wL²/2 | V_max = wL
δ_max = wL⁴/8EI (at free end)

Uniform Load (w) - plf

Length (L) - ft

E (psi)

I (in⁴)

Results

Max Moment (at fixed end)

—

Reaction (R) —

Fixed End Moment —

Max Shear —

Max Deflection (at tip) —

Deflection Ratio (L/δ) —

Slope at Tip —

Triangular Load (Max at Fixed End)

₀ L

M_max = w₀L²/6 | V_max = w₀L/2
δ_max = w₀L⁴/30EI

Max Load Intensity (w₀) - plf

Length (L) - ft

E (psi)

I (in⁴)

Results

Max Moment (at fixed end)

—

Total Load —

Reaction (R) —

Max Deflection —

Deflection Ratio (L/δ) —

Note: Triangular loading is common for soil pressure on retaining walls or hydrostatic pressure applications.

Cantilever Design Check

Check a cantilever beam for bending, shear, and deflection.

Member Size

S_x (in³)

I_x (in⁴)

Length (ft)

Load Type

Load Value (lb for point, plf for uniform)

F_b Allowable (psi)

E (psi)

Deflection Limit

Results

Overall Status

—

Bending Stress (f_b) —

Bending Check —

Actual Deflection —

Allowable Deflection —

Deflection Check —

Max Moment —

Cantilever Beam Formulas

Loading	Max Moment	Max Shear	Max Deflection (at tip)
Point P at End	PL	P	PL³/3EI
Point P at distance a	Pa	P	Pa²(3L-a)/6EI
Uniform w over L	wL²/2	wL	wL⁴/8EI
Uniform w over length a	wa²/2	wa	wa²(4L-a)/24EI
Triangular (max at support)	w₀L²/6	w₀L/2	w₀L⁴/30EI
Moment M at End	M	0	ML²/2EI