By Zencalcy Editorial TeamLast reviewed About us
A simply supported beam rests on two supports, usually a pin at one end and a roller at the other. For a single downward point load, the two reactions share the load in inverse proportion to their distance from it: the nearer support carries more.
Support reactions for a simply supported beam with a point load.
R₁ = P (L − a) / L R₂ = P a / L
R₁ is the left reaction, R₂ the right, P the point load, L the span and a the load's distance from the left support. The beam's own weight is ignored.
| Symbol | Meaning |
|---|---|
| R₁, R₂ | Reaction forces at the left and right supports, in newtons. |
| P | Point load, in newtons. |
| L | Span between supports, in metres. |
| a | Distance from the left support to the load, in metres. |
The left support carries 1,000 × (6 − 2) / 6 = 666.7 N and the right carries 1,000 × 2 / 6 = 333.3 N. Together they equal the 1,000 N load.
Continue with the Center of Mass Calculator, Hooke's Law Calculator, or the Hydraulic Press Calculator — or browse more statics tools and all physics calculators.
Taking moments about one support shows that the other reaction is proportional to the load's distance from the opposite support. A load near the left support is mostly carried by the left one.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026