Cantilever Beam Tip Deflection Calculator
Euler-Bernoulli beam theory determines the vertical tip deflection δ of a cantilevered beam of length L, flexural modulus E, and second moment of area I subjected to a concentrated end load F: δ = (F × L³) / (3 × E × I).
Vertical downward tip displacement in millimeters
Point load applied at the free end in Newtons
Unsupported beam overhang length in meters
Material modulus of elasticity in Gigapascals (Steel = 200 GPa)
Cross-sectional second moment of area in cm⁴ (1 cm⁴ = 10⁻⁸ m⁴)
Step-by-Step Calculation
Euler-Bernoulli beam theory determines the vertical tip deflection δ of a cantilevered beam of length L, flexural modulus E, and second moment of area I subjected to a concentrated end load F: δ = (F × L³) / (3 × E × I).
Real-World Reference Values
Standard rolled wide-flange I-beam modulus
Deflects 2.9× more than an identical steel section
IBC structural deflection limit for overhangs
20-Row Comparison Table
Maximum Tip Deflection (mm) (δ (mm)) · Concentrated Tip Load (F)
| # | Concentrated Tip Load (N) | Maximum Tip Deflection (mm) (δ (mm)) | Δ % |
|---|---|---|---|
| 01 | 1 N | 0.001333 | -99.98% |
| 02 | 4,000.00 NCurrent | 5.3333 | 0.00% |
| 03 | 14,895.62 N | 19.8608 | +272.39% |
| 04 | 22,342.93 N | 29.7906 | +458.57% |
| 05 | 29,790.23 N | 39.7203 | +644.76% |
| 06 | 37,237.54 N | 49.6501 | +830.94% |
| 07 | 44,684.85 N | 59.5798 | +1017.12% |
| 08 | 52,132.16 N | 69.5095 | +1203.30% |
| 09 | 59,579.47 N | 79.4393 | +1389.49% |
| 10 | 67,026.78 N | 89.369 | +1575.67% |
| 11 | 74,474.09 N | 99.2988 | +1761.85% |
| 12 | 81,921.39 N | 109.2285 | +1948.03% |
| 13 | 89,368.70 N | 119.1583 | +2134.22% |
| 14 | 96,816.01 N | 129.088 | +2320.40% |
| 15 | 104,263.32 N | 139.0178 | +2506.58% |
| 16 | 111,710.63 N | 148.9475 | +2692.77% |
| 17 | 119,157.94 N | 158.8772 | +2878.95% |
| 18 | 126,605.25 N | 168.807 | +3065.13% |
| 19 | 134,052.55 N | 178.7367 | +3251.31% |
| 20 | 141,499.86 N | 188.6665 | +3437.50% |
Frequently Asked Questions
Why does doubling cantilever length L increase deflection by 8×?+
Tip deflection scales with the cube of span length (L³), so 2³ = 8 times greater deflection for the same tip load.
How do I size the required beam moment of inertia I (cm⁴) to stay under L/240?+
Click SOLVE FOR on I (cm⁴) and set δ (mm) to your maximum allowable deflection in millimeters.
How does a uniformly distributed load compare to a tip point load?+
If the same total load W is distributed uniformly along the beam (δ = WL³ / 8EI), tip deflection is 3/8 (37.5%) of the end-point load deflection.