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Beam and Joist Point Load Moment Calculator (Equivalent UDL)

The maximum moment in a simply supported beam or joist under a uniform load plus a point load, where it peaks, the reactions and the equivalent UDL.

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  • Every formula cited
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The clear span, support to support.

The distance between the centres of bearing, which is slightly more than the clear opening.

The load spread evenly along the span — self-weight, floor load on this member's share, a wall on it.

A floor load per square metre becomes a joist's line load when multiplied by the width of floor the joist carries: 1.5 kN/m² (31 psf) on joists at 400 mm (16 in) centres is 0.6 kN/m (41 lbf/ft).

A load concentrated at one place along the span — a post, a retained chimney breast, a tank's leg.

A load that sits across a short length, such as a chimney breast bearing across its own width, is close enough to a point load for screening when that length is small against the span.

Where along the span the point load sits, measured from one support.

At mid-span it bends the beam most; near a support it goes almost straight into the support and bends it little.

Maximum bending moment

10.2 kip·ft

High confidence

A demand, not a capacity. The section that carries it is checked separately for bending, for shear at the larger reaction, and for deflection, which on a beam holding up masonry or plaster usually decides the size before strength does. The equivalent uniform load matches the point load on bending and over-states its deflection, so it is a screening figure for a table written in uniform loads, never a design.

Where the moment peaks, from the left support
6.5 ft
Left reaction
2.01 kips
Right reaction
2.01 kips
Moment from the point load alone
7.31 kip·ft
Uniform load that bends the beam as much as the point load
345.86 lbf/ft
End shear the point load puts into the nearer support
1.12 kips
End shear the equivalent uniform load gives
2.25 kips
The two maxima added (safe-side shortcut)
10.2 kip·ft
Then change the inputs to see how far the answer moves.

Show calculation logic

How this was calculated

Formula source(s)

  • Simply supported beam (AISC Steel Construction Manual, Table 3-23, beam diagrams 1 and 7): a uniform load w gives R = wL/2 at each end and M = wL²/8 at mid-span; a point load P at a from one end and b from the other gives R1 = Pb/L, R2 = Pa/L and M = Pab/L under the load; combined, the moment peaks where the shear crosses zero
  • The uniform load giving the same peak moment as the point load alone: w = 8Pab ÷ L³, which is 2P ÷ L for a load at mid-span

Inputs used

Span Between Supports
13 ft
Uniform Load Along the Beam
137.04 lbf/ft
Point Load
2.25 kip
Distance of the Point Load from the Left Support
6.5 ft

Intermediate steps

Where the moment peaks, from the left support
6.5 ft
Left reaction
2.01 kips
Right reaction
2.01 kips
Moment from the point load alone
7.31 kip·ft
Uniform load that bends the beam as much as the point load
345.86 lbf/ft
End shear the point load puts into the nearer support
1.12 kips
End shear the equivalent uniform load gives
2.25 kips
The two maxima added (safe-side shortcut)
10.2 kip·ft
Final result10.2 kip·ft

Confidence note: A demand, not a capacity. The section that carries it is checked separately for bending, for shear at the larger reaction, and for deflection, which on a beam holding up masonry or plaster usually decides the size before strength does. The equivalent uniform load matches the point load on bending and over-states its deflection, so it is a screening figure for a table written in uniform loads, never a design.

What this calculation does not cover

  • One span, simply supported, with one point load. A continuous beam, a cantilever or several point loads need their own analysis.
  • The loads are taken as given, with no factors. Characteristic loads give a working moment; a limit-state design applies the partial factors of the code in force before the section is checked.
  • A load spread over a length that is a real share of the span — a wide chimney breast on a short beam — is a patch load, whose peak moment is lower than the point load's; treating it as a point is on the safe side.

Add the equipment this sizes

This result is a specification — 10.2 kip·ft — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.

13 ft
Schematic, drawn to the proportions you entered — not to scale on screen.

Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.

Sources checked 2026-09-22 · v1.0.0

Regulatory standards & verification citations2
  1. Simply supported beam (AISC Steel Construction Manual, Table 3-23, beam diagrams 1 and 7): a uniform load w gives R = wL/2 at each end and M = wL²/8 at mid-span; a point load P at a from one end and b from the other gives R1 = Pb/L, R2 = Pa/L and M = Pab/L under the load; combined, the moment peaks where the shear crosses zero
  2. The uniform load giving the same peak moment as the point load alone: w = 8Pab ÷ L³, which is 2P ÷ L for a load at mid-span
Cite this page

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Now that you have the number

These guides cover the work this quantity is for.

How to calculate beam and joist point load moment (equivalent UDL) in 5 steps

  1. Span Between SupportsThe clear span, support to support.
  2. Uniform Load Along the BeamThe load spread evenly along the span — self-weight, floor load on this member's share, a wall on it.
  3. Point LoadA load concentrated at one place along the span — a post, a retained chimney breast, a tank's leg.
  4. Distance of the Point Load from the Left SupportWhere along the span the point load sits, measured from one support.
  5. Maximum bending momentThe tool computes the maximum bending moment from those figures and shows the formula, its sources, and a confidence rating alongside it.

Maximum bending moment by span between supports

Page defaults, not your figures above.

Span Between SupportsMaximum bending moment (kip·ft)
10 ft6.62
15 ft12.1
20 ft16
25 ft19.4

Frequently asked questions

Why convert a point load to an equivalent uniform load?
Because published lintel and beam safe-load tables are written for uniform loads. The uniform load that gives the same peak moment as a point load P at mid-span is 2P ÷ L, since PL/4 = wL²/8; off-centre it is 8Pab ÷ L³. It is exact on bending and high on deflection wherever the load sits, a quarter high at mid-span and more towards a support. End shear is where it misleads: twice the point load's at mid-span, equal at a quarter of the span, and lower nearer a support — at a tenth of the span, 40 per cent of it. The page gives both end shears, and the equivalent load is a screening figure, never a design.
Where does the maximum moment occur?
Where the shear force crosses zero. With a point load alone that is under the load; with a uniform load alone it is mid-span; with both, it is under the point load or between it and mid-span, and the page finds which.
Can I just add the two maximum moments?
Only as a safe-side shortcut. The uniform load peaks at mid-span and an off-centre point load under itself, so the true peak is lower than their sum: 2 kN/m (137 lbf/ft) on a 4 m (13 ft 1 in) span with 10 kN (2.25 kip) at 1 m (3 ft 3 in) peaks at 10.5 kN·m (7.7 kip·ft), not the 11.5 (8.5) the sum gives.
What about a load on a single joist in a floor?
Work out the worst joist on its own: its share of the floor load as a uniform load, plus any foot or leg that lands within its span as a point load. A load set across several joists spreads between them; the same load along one joist line is carried by that joist and its neighbours.
Preliminary estimate, not certified engineering. This tool produces an indicative quantity calculation for planning purposes only — it is not a certified structural analysis, a guaranteed material takeoff, or a substitute for building department approval. Always verify measurements on-site and have a licensed contractor or structural engineer review any load-bearing, code-sensitive, or safety-critical work before purchasing materials or starting construction. Spotted an arithmetic or standards error? Report it to contact@craftquantities.com with your inputs — a confirmed fix gets a permanent check of its own, so the same mistake cannot come back.