OneTaskBy Tim King · Updated
Beam Load Calculator
Bending Stress and Deflection of a Beam
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How the Beam Load Calculator works
This beam load calculator gives a rough check of a rectangular beam or joist supported at both ends and carrying an even load. Enter the span, the width and depth of the section, the load per metre and the material, and it returns the bending moment, the bending stress compared with the material's strength, and the mid-span deflection compared with span/250.
A beam fails in one of two ways: it bends so much it cracks or yields (strength), or it sags enough to crack ceilings and feel bouncy (stiffness). For timber joists the deflection limit usually decides the size, not the strength. Depth matters far more than width: doubling the depth makes a beam four times stronger and eight times stiffer.
How the beam load calculator works
The formula for a simply supported beam under a uniform load w over span L is: moment M = wL²/8; stress = M ÷ (bd²/6); deflection = 5wL⁴ ÷ (384 E I), where I = bd³/12. For example, a 47 × 200 mm C24 joist over 4 m carrying 2 kN/m has a moment of 4.00 kNm, a stress of 12.8 N/mm² (53% of 24) but deflects 19.3 mm, more than the 16 mm span/250 limit, so it needs to be deeper or closer together. A second example: a 75 × 225 mm C16 beam over 3 m at 3 kN/m uses 33% of its strength and deflects 5.6 mm against a 12 mm limit.
To find the load per metre on a joist, multiply the floor load in kN/m² by the joist spacing in metres; a domestic floor is often designed for about 1.5 kN/m² imposed plus its own weight. This is a simplified check that ignores load duration, safety factors, notches and point loads, so use it to see roughly how many millimetres of depth you need, then have any real beam sized by an engineer or from official span tables.
Deflection of a 47 mm wide C24 joist under 2 kN/m, by span and depth (mm, limit span/250)
| Span | Limit | 47 × 150 | 47 × 175 | 47 × 200 | 47 × 225 | 47 × 250 |
|---|---|---|---|---|---|---|
| 2.0 m | 8.0 | 2.9 | 1.8 | 1.2 | 0.8 | 0.6 |
| 2.2 m | 8.8 | 4.2 | 2.6 | 1.8 | 1.2 | 0.9 |
| 2.4 m | 9.6 | 5.9 | 3.7 | 2.5 | 1.8 | 1.3 |
| 2.6 m | 10.4 | 8.2 | 5.2 | 3.5 | 2.4 | 1.8 |
| 2.8 m | 11.2 | 11.0 | 6.9 | 4.6 | 3.3 | 2.4 |
| 3.0 m | 12.0 | 14.5 | 9.1 | 6.1 | 4.3 | 3.1 |
| 3.2 m | 12.8 | 18.8 | 11.8 | 7.9 | 5.6 | 4.1 |
| 3.4 m | 13.6 | 23.9 | 15.1 | 10.1 | 7.1 | 5.2 |
| 3.6 m | 14.4 | 30.1 | 18.9 | 12.7 | 8.9 | 6.5 |
| 3.8 m | 15.2 | 37.3 | 23.5 | 15.8 | 11.1 | 8.1 |
| 4.0 m | 16.0 | 45.8 | 28.9 | 19.3 | 13.6 | 9.9 |
| 4.2 m | 16.8 | 55.7 | 35.1 | 23.5 | 16.5 | 12.0 |
| 4.4 m | 17.6 | 67.1 | 42.3 | 28.3 | 19.9 | 14.5 |
| 4.6 m | 18.4 | 80.2 | 50.5 | 33.8 | 23.8 | 17.3 |
| 4.8 m | 19.2 | 95.1 | 59.9 | 40.1 | 28.2 | 20.5 |
| 5.0 m | 20.0 | 111.9 | 70.5 | 47.2 | 33.2 | 24.2 |
| 5.2 m | 20.8 | 130.9 | 82.5 | 55.2 | 38.8 | 28.3 |
| 5.4 m | 21.6 | 152.3 | 95.9 | 64.2 | 45.1 | 32.9 |
| 5.6 m | 22.4 | 176.1 | 110.9 | 74.3 | 52.2 | 38.0 |
| 5.8 m | 23.2 | 202.7 | 127.6 | 85.5 | 60.1 | 43.8 |
| 6.0 m | 24.0 | 232.1 | 146.2 | 97.9 | 68.8 | 50.1 |
FAQ
How do I calculate the load on a beam?
Add the weight of the floor or roof it carries (dead load) to the use load (imposed load), both in kN per square metre, then multiply by the width of floor each beam supports. For joists at 400 mm centres carrying 2 kN/m² in total, that is 0.8 kN per metre of joist.
What is the deflection limit for floor joists?
A common limit for domestic floors is span/250 under full load, or span/333 in some codes, and often an absolute cap of around 14 mm. Stricter limits such as span/360 apply under plaster ceilings and tiled floors so that finishes do not crack.
Can I use this to size a steel beam?
Only as a first rough check. Steel beams are I-sections, not solid rectangles, and are sized from their published section properties with safety factors and lateral buckling checks. Building control will want calculations from a structural engineer for any steel beam.
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