Calculator
Select a physics case, enter the known values, and press calculate. The result appears above this form.
Formula Used
Flat surface
R = m(g + a) + F↓ − F↑
Use this when a body rests on a horizontal surface and may also accelerate vertically. Upward applied forces reduce the surface reaction. Downward applied forces increase it.
Inclined plane
R = mg cos(θ) + Finward − Foutward
Only force components perpendicular to the plane affect the normal reaction. The cosine term captures the gravity component normal to the slope.
Simply supported beam
ΣFy = 0, ΣM = 0
RB = ΣMleft / L
RA = Total Load − RB
How to use this calculator
- Select the reaction type: flat surface, inclined plane, or beam support.
- Enter all known values in the visible fields.
- Choose units and decimal precision that match your problem.
- Press the calculate button to show the result section above the form.
- Read the summary cards, detailed table, and graph for interpretation.
- Use the CSV or PDF buttons to save the current calculation output.
Example data table
| Scenario | Inputs | Output |
|---|---|---|
| Flat surface | m = 20 kg, g = 9.81 m/s², a = 0, F↑ = 40 N, F↓ = 0 | R = 156.20 N |
| Inclined plane | m = 15 kg, θ = 30°, g = 9.81 m/s², inward = 20 N | R = 147.44 N |
| Beam | L = 6 m, P1 = 12 kN at 2 m, P2 = 8 kN at 4.5 m, UDL = 1.5 kN/m | RA = 14.50 kN, RB = 14.50 kN |
FAQs
1. What is a reaction force?
A reaction force is the support or contact force produced by a surface or support when a body applies a load to it. It helps satisfy equilibrium or motion constraints.
2. Why can the calculator show zero reaction?
A zero displayed reaction means the raw equation predicted a negative contact force. Physically, that suggests the object would lose contact rather than pull on the surface.
3. Does friction change the normal reaction?
Not directly in these models. Friction acts parallel to the surface, while the normal reaction acts perpendicular to it. Only perpendicular components affect the normal reaction value here.
4. When should I use the incline mode?
Use incline mode when the body rests on a sloped plane and you need the force normal to the surface. It is especially useful for ramps, wedges, and textbook statics problems.
5. What assumptions are used for the beam mode?
The beam mode assumes a simply supported beam with ideal supports, static loading, two optional point loads, and one full-span uniformly distributed load.
6. Can I enter different units?
Yes. Surface and incline modes can display results in newtons, kilonewtons, or pounds-force. Beam mode lets you label force and length units consistently for the entered loads.
7. Why is the beam equilibrium check important?
It confirms that the computed reactions add up correctly against the total load. A value near zero indicates the force balance is internally consistent.
8. Is this calculator suitable for final design work?
It is best for study, estimation, and quick verification. Final engineering design should also consider standards, safety factors, boundary conditions, and professional review.