Beam Load Calculator

How to use this beam load calculator

What this calculator does

This calculator estimates the vertical support reactions for a simply supported beam carrying discrete point loads. It applies the two static-equilibrium conditions: the sum of vertical forces is zero and the sum of moments about a support is zero. The model treats the beam as weightless and rigid for the purpose of finding reactions. It does not size the beam, check bending stress, shear stress, deflection, buckling, bearing, connections, or code compliance. Those design checks require material properties, cross-section data, load combinations, safety factors, and applicable standards.

When to use it

Use it to check reactions for a preliminary free-body diagram, split point loads between two end supports, verify hand calculations for statics coursework, or estimate the forces transferred into columns, walls, bearings, or foundations before detailed structural analysis. For a refresher on the governing principles, see the OpenStax explanation of conditions for static equilibrium.

How to calculate

1. The calculator opens with a complete demonstration: a 4 m span, a 10 kN load at 2 m, and a 3.5 kN load at 2.5 m. Its results and XLSX workbook are ready immediately.
2. Select the Unit system. Metric uses kilonewtons and metres; Imperial uses pounds-force and feet. Switching systems converts the current values rather than relabelling them.
3. Enter the Span, L, then choose the Number of loads. Complete each visible Load n, Fₙ and Distance from A, xₙ field. Results update live.
4. Read Support reaction at A, Support reaction at B, the total load, total moment, resultant location, and the contribution table. Use Download Excel to export the current validated state.
5. Reset clears the demonstration and calculated content. Download Excel is then disabled until a complete valid state is entered again.

Input guide

Unit system is required and accepts Metric (kN, m) or Imperial (lbf, ft). A typical structural sketch might use metric values such as 4 m and 10 kN. Changing it converts span, distances, loads, reactions, and moments. Do not switch units and then manually re-enter already converted numbers unless that is intentional.

Span, L is a required positive decimal representing the clear distance between supports A and B. Enter plain en-US decimal notation, such as 4 or 12.5; commas, scientific notation, and unit text are rejected. A larger span changes the lever-arm ratio and therefore the reaction split. A zero or negative span is invalid.

Number of loads is required and accepts an integer from 1 to 10. Increasing it reveals additional rows. Reducing it removes inactive rows from the model and export. Each Load n, Fₙ is a required signed decimal force. Positive values act downward; negative values model uplift. For example, 10 kN is downward and – 2 kN is upward. Each Distance from A, xₙ is required, must be between zero and the span inclusive, and uses the active length unit. A load at zero acts directly at A; a load at the full span acts directly at B. A common mistake is entering distance from support B instead of A.

Output guide

Support reaction at A, Rₐ and Support reaction at B, Rᵦ are signed vertical forces. Positive values mean upward support action under the calculator's sign convention; negative values indicate hold-down or uplift demand. Total applied load, ΣF is the signed sum of all point loads. Moment about A, Σ(F × x) sums every force multiplied by its distance from A. Resultant load location from A equals total moment divided by total force when the signed total is not zero; it is reported as not applicable when opposing loads cancel. The Equilibrium check confirms that Rₐ + Rᵦ matches ΣF within numerical precision.

The Load contribution table lists each force, its distance, its moment contribution, and its signed share of total force. These are exact identities from the entered point-load model, not recommendations. High reaction at one support means the load system's resultant lies closer to that support. A zero reaction means the resultant passes through the other support. A negative reaction indicates uplift restraint may be needed.

Worked example

For the startup example, the total moment about A is (10 × 2) + (3.5 × 2.5) = 28.75 kN·m. Dividing by the 4 m span gives Rᵦ = 7.1875 kN. Force equilibrium then gives Rₐ = 10 + 3.5 – 7.1875 = 6.3125 kN. The reactions add to 13.5 kN, exactly matching the total applied load. This is the same first-open result shown on the page and stored in the downloadable workbook.