Beam Reaction Calculator
Calculate the support reactions of a simply supported (or overhanging) beam under point loads and a uniformly distributed load, using static equilibrium (ΣF = 0, ΣM = 0). Flags a negative reaction as uplift, where the support would need to be anchored down.
Input
Labels the results only — enter every load in this same unit.
Supports
Distance from the beam's left end (x = 0).
Distance from the beam's left end. Set either support inside the beam's ends to model an overhang.
Force per unit length, downward-positive. Leave 0 to skip.
Downward-positive. Leave 0 to skip.
Downward-positive. Leave 0 to skip.
Output
| Property | Value |
|---|---|
| No data yet | |
| Load | Magnitude | Position | Arm from A |
|---|---|---|---|
| No data yet | |||
Every load counted toward the reactions above, with its distance from Support A.
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/beam-reaction-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"beamLength": "10",
"lengthUnit": "m",
"forceUnit": "kN",
"supportAPosition": "0",
"supportBPosition": "10",
"udlMagnitude": "0",
"udlStart": "0",
"udlEnd": "10",
"pointLoad1Magnitude": "20",
"pointLoad1Position": "5",
"pointLoad2Magnitude": "0",
"pointLoad2Position": "5"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `beam-reaction-calculator` tool (Beam Reaction Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/beam-reaction-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Beam Reaction Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
Also available with
Guides
Beam Reaction Calculator finds the support reactions of a simply supported or overhanging beam carrying point loads and/or a uniformly distributed load, using the two static-equilibrium equations every statically-determinate beam problem starts from: ΣF = 0 and ΣM = 0. No signup, and everything runs instantly in your browser.
How to use it
- Enter the beam length and pick a length/force unit.
- Set Support A and Support B positions, measured from the beam's left end. Leave them at the two ends for a standard simply supported beam, or move either one inward to model an overhanging beam.
- Open Distributed load and/or Point loads and fill in whichever loads your beam actually carries — leave a magnitude at
0to skip it. - Read the reactions, the equilibrium breakdown, and the per-load table showing each load's distance from Support A.
The math
For a beam with only two supports and no applied moments, the system is statically determinate — the two reactions are fully solved by:
- Sum of moments about Support A = 0:
R_B × (x_B − x_A) = Σ(load × distance from A) - Sum of vertical forces = 0:
R_A + R_B = Σ(loads)
A uniformly distributed load is converted to its statically-equivalent point load first — total magnitude w × length, acting at the load's midpoint — then combined with any point loads before applying the two equations above. This is the same superposition every hand calculation uses, so the tool's breakdown table doubles as a check on your own work.
What if a reaction comes out negative?
A negative reaction means that support would have to pull down on the beam to keep it in equilibrium — physically, a plain pin or roller resting under the beam can only push up. The tool flags this as uplift: it usually means the beam is overhanging far enough, or carrying enough load past one support, that the other support needs to be a proper anchor (a bolted-down connection) rather than a simple bearing.
Does this handle a fixed (cantilever) support?
No — this tool solves the standard two-support, statically-determinate case (simply supported or overhanging). A beam fixed at one end and free at the other (a cantilever) or fixed at both ends is statically indeterminate and needs a different method (e.g. moment-distribution or a stiffness/FEA approach) to solve, which is out of scope here.
Does it account for the beam's own weight?
No — like most reaction calculators, this treats the beam as weightless. If your beam's self-weight is significant relative to the applied loads, add it as an extra uniformly distributed load (its weight per unit length) spanning the full beam.
Everything is computed client-side — nothing you enter is sent anywhere.