Reaction Force Calculator

Solve reaction forces for blocks, ramps, and lifts. Find beam support reactions from multiple loads. Download clean CSV and PDF summaries for sharing easily.

Calculator

Choose a model and enter values

Use consistent units. Forces are in newtons.
Pick the setup closest to your problem.
Used in downloads, not the on-page table.
Optional external force.
Angle above the plane (perpendicular component).
Used for the maximum static friction limit μN.
Example data

Example input and output table

Scenario Key inputs Key outputs
Normal reaction on an incline m=20 kg, g=9.81, θ=30°, P=0, μ=0.35 N≈169.914, μN≈59.470
Normal reaction with pull-away force m=15 kg, θ=0°, P=80 N, φ=90°, away, μ=0.20 N≈67.100, μN≈13.420
Beam reactions with UDL L=6 m, w=200 N/m, no point loads RA=600.000, RB=600.000
Beam reactions with point loads L=5 m, P1=500 N at x=2 m, P2=300 N at x=4 m RA=420.000, RB=380.000
Numbers are rounded for display in this example table.
Formula used

Equations behind the calculations

Normal reaction (block on plane)

The component of weight perpendicular to the plane is m g cos(θ). An applied force P at angle φ above the plane contributes ± P sin(φ) to the perpendicular direction.
  • N = m g cos(θ) ± P sin(φ)
  • F_max = μ N (maximum static friction limit)
If the computed N is negative, the model reports lift-off and sets N = 0.

Simply supported beam reactions

For span L with point loads P_i at x_i and a uniform load w across the full span:
  • W = w L and acts at L/2
  • Moments about A: R_B L = Σ(P_i x_i) + W (L/2)
  • Vertical balance: R_A + R_B = ΣP_i + W
How to use

Steps

  1. Select a model: block/plane for normal reaction, or beam for support reactions.
  2. Enter values using consistent units: kg, m, seconds, and newtons.
  3. Press Submit to calculate. Results appear above the form.
  4. Use Download CSV or Download PDF for sharing or archiving.
  5. If lift-off is reported, reduce pull-away force or adjust geometry.
Tip: For beam problems, keep load locations between 0 and L.
Article
Word count: 370 (including headings).

Load paths and reaction force budgeting

For a simply supported 5.0 m beam with a 500 N load at x = 2.0 m, moments give RB = (500×2)/5 = 200 N and RA = 300 N. Adding a 300 N load at x = 4.0 m shifts reactions to RA = 420 N and RB = 380 N.

Inclined contact and normal force scaling

For a block on a plane, the perpendicular weight component governs contact: N = m g cosθ. With m = 20 kg and g = 9.81 m/s², N is about 196.2 N at θ = 0°, 169.9 N at 30°, and 98.1 N at 60°. As θ rises, contact pressure and friction capacity drop even if mass is unchanged.

Auxiliary forces and lift off thresholds

External forces change N through the perpendicular component, P sinφ. With m = 15 kg on level ground, weight alone gives N ≈ 147.1 N. A pull-away P = 80 N at φ = 90° reduces N to about 67.1 N, while a push toward the surface raises N to about 227.1 N. If N becomes negative, lift-off occurs and contact is lost.

Friction capacity and verification margins

Maximum static friction is limited by Fmax = μN. Using μ = 0.35 with N ≈ 169.9 N yields Fmax ≈ 59.5 N. If tangential demand is 45 N, the margin is 59.5/45 ≈ 1.32. When μ is uncertain, check a range such as 0.20 to 0.45 to see sensitivity.

Distributed loads and support balance

Uniformly distributed loads reduce to an equivalent force W = wL acting at midspan. For L = 6 m and w = 200 N/m, W = 1200 N at x = 3 m. Symmetry produces RA = RB = 600 N. With point loads, the calculator combines Σ(Pi xi) with W(L/2) to preserve moment balance.

Reporting, rounding, and engineering traceability

Results are strongest when assumptions are explicit: geometry, load directions, units, and rounding. Exporting CSV supports quick checks, while PDF provides a stable record for reviews. Adjust one variable at a time, then compare reaction shifts to component ratings, anchor capacities, and allowable bearing pressures. For audits, note input sources and keep a versioned calculation date in reports.

FAQs

Questions and answers

What does the normal reaction represent?

It is the contact force perpendicular to the surface that prevents interpenetration. It balances the perpendicular components of weight and any applied forces when the body remains in contact.

Why can the calculator show lift-off?

If an applied pull-away component exceeds the perpendicular weight component, the computed normal reaction becomes negative. That indicates the surface cannot “pull” the object, so contact is lost and N is set to zero.

Does friction change the normal reaction here?

In this simplified model, friction is tangential and does not alter the perpendicular balance. The calculator uses N to compute the maximum static friction limit μN for quick feasibility checks.

When should I use the beam model?

Use it for statically determinate, simply supported beams where reactions at two supports are found from force balance and moments. It supports a full-span uniform load plus up to three point loads.

What units should I use?

Use kilograms, meters, and seconds with forces in newtons. Keep locations between 0 and L. Consistent units ensure reactions and friction limits are reported correctly.

How accurate are the exports?

CSV and PDF exports reflect the computed tables and your selected rounding for downloads. Accuracy depends on correct inputs, geometry assumptions, and whether the real system matches the idealized static models.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.