Open almost any structural calculation and you will find a number with the units kN/m sitting next to a beam. It is the single most common way structural and mechanical engineers describe a load that is smeared out along a length rather than dumped at a point: the self-weight of a beam, the floor it carries, the wall sitting on top of it, the snow on the roof. Get the kN/m value right and the rest of the beam design — reactions, shear, bending moment, deflection — follows almost mechanically. Get it wrong, usually by confusing it with an area load in kN/m² or with a linear mass density in kg/m, and every downstream number is wrong too. This article explains what a kN/m line load actually is, where the number comes from, how it converts into beam reactions and moments, and the unit conversions engineers reach for most — including the lb/ft-versus-kg/m trap that catches people who mix force-per-length with mass-per-length.

Point load, line load, area load: three different things

Loads in structural engineering come in three dimensional flavours, and keeping them straight is half the battle:

  • Point load (concentrated load), units kN. A single force applied at essentially one location — a column landing on a beam, a wheel load, a hung piece of equipment. It is just a force, so its unit is the kilonewton on its own. The kilonewton is 1,000 newtons, or about 224.8 lbf, and as a rough mental anchor 1 kN is roughly the weight of a 102 kg mass under standard gravity.
  • Line load (distributed load), units kN/m. A force spread along a line — force per unit length. A uniformly distributed load (UDL) of 15 kN/m means every metre of the member carries 15 kN. This is the subject of the article and the quantity you feed into a beam calculation as the symbol w (or sometimes q).
  • Area load (pressure / surface load), units kN/m². A force spread over a surface — force per unit area. Floor live loads, roof loads, and wind pressures are quoted this way: an office floor might be designed for 2.5 kN/m², a snow load for 1.5 kN/m². An area load is not something a beam can use directly; it has to be turned into a line load first, which is where tributary width comes in.

The trap is the little superscript. kN/m (per metre, force per length) and kN/m² (per square metre, force per area) look almost identical on a drawing and differ by a single character, but they are dimensionally different quantities. A beam wants kN/m; a slab or a wind face is described in kN/m². Mixing them is one of the most common and most consequential mistakes in load take-down, and it is worth reading every load on a drawing twice for exactly that reason.

Where the kN/m number actually comes from

A line load on a beam is rarely given to you directly. It is almost always assembled from several sources, each of which you compute and then sum into a single design w. The usual contributors are:

  • Self-weight of the member. A rolled steel section is catalogued by its mass per unit length — an IPE 400 is 66.3 kg/m, a W14×90 is 90 lb/ft. Multiplying that mass per length by gravity g ≈ 9.81 m/s² turns it into a force per length: 66.3 kg/m × 9.81 m/s² ≈ 650 N/m ≈ 0.65 kN/m. For a concrete or timber member you instead take the material’s density (kN/m³) and multiply by the cross-sectional area (m²), which again lands in kN/m. Self-weight is the textbook example of why mass per length and force per length are not the same number, separated by a factor of g.
  • Floor and roof loads via tributary width. This is the big one. A floor delivers its load to a beam as an area load in kN/m², and the beam picks up everything within its tributary width — half the span to the next parallel beam on each side. Multiply the area load (kN/m²) by the tributary width (m) and the square metres collapse into a line load in kN/m: a 5 kN/m² floor with a 4 m tributary width puts 5 × 4 = 20 kN/m onto the beam. Forgetting the tributary-width step — feeding the raw kN/m² straight into a beam — is the classic units error in this whole topic.
  • Wall and cladding loads. A masonry wall or a glazed curtain wall sitting on top of a beam contributes a line load equal to its weight per square metre of elevation times its height. A 3 m tall wall weighing 2.5 kN/m² of face area adds 2.5 × 3 = 7.5 kN/m along the supporting beam.
  • Snow and wind as line loads. Snow and wind start life as area loads (kN/m² on a roof or wall), but once you apply the relevant tributary width or panel width they too become kN/m line loads on the member that carries them — exactly the same tributary-width arithmetic as a floor.

In a real design these are combined with load factors (1.35 on permanent actions and 1.5 on variable actions in Eurocode, or the various combinations in ASCE 7) before being summed, but the units bookkeeping is the same: everything ends up as a single factored w in kN/m before it touches a beam formula.

From a UDL to reactions, shear, and moment

Once you have a uniform line load w (kN/m) acting over a span L (m), the beam results fall out of a handful of standard formulae. The total load carried is simply the area under the load diagram — the rectangle w × L — and it acts at the centroid of that rectangle, the mid-span. For the two cases you will meet most often:

  • Simply supported beam, UDL over the whole span. Total load = w·L. By symmetry each support carries half, so the reactions are R = wL/2 at each end. The shear is maximum at the supports (equal to the reaction) and zero at mid-span; the bending moment is maximum at mid-span with the famous value Mmax = wL²/8.
  • Cantilever, UDL over the whole length. The whole load wL is reacted at the single fixed support, so the reaction is R = wL and the maximum bending moment is at the fixed end with Mmax = wL²/2 — four times the simply supported moment for the same w and L, which is exactly why cantilevers feel so much more demanding.

Note the structure of those moment formulae: the load w enters linearly but the span L enters as a square. Doubling the load doubles the moment; doubling the span quadruples it. That L² dependence is the single most important intuition in beam design, and it is why long spans are so much more punishing than heavy loads. The beam bending calculator applies these reaction and moment formulae directly for simply supported, cantilever, and fixed-fixed cases, so you can check the hand-calculation below against it.

Worked example: a simply supported beam under 15 kN/m

Take a simply supported beam spanning L = 6 m and carrying a uniformly distributed load w = 15 kN/m (say a factored combination of self-weight, floor dead load, and floor live load already summed). Find the total load, the support reactions, and the maximum bending moment.

Step 1 — total load. The total downward force is the area of the load rectangle:

  • Wtotal = w · L = 15 kN/m × 6 m = 90 kN

Step 2 — reactions. The beam and its load are symmetric, so each support carries exactly half the total:

  • RA = RB = wL/2 = 90 / 2 = 45 kN at each end

The maximum shear force in the beam equals the reaction, Vmax = 45 kN, occurring just inside each support.

Step 3 — maximum bending moment. For a simply supported UDL the maximum moment is at mid-span:

  • Mmax = wL²/8 = 15 × 6² / 8 = 15 × 36 / 8 = 540 / 8 = 67.5 kN·m

So a 6 m beam under 15 kN/m gives 90 kN total, 45 kN reactions, and 67.5 kN·m of mid-span moment. That moment is the number you carry into a section-sizing check: divide it by the allowable bending stress to get the required section modulus, or feed it straight into a stress check with the beam stress calculator (σ = M·y/I) to confirm the chosen section stays below its limit. As a sanity check on the L² effect: had the same 15 kN/m acted on the same beam configured as a 6 m cantilever instead, the moment would be wL²/2 = 270 kN·m — exactly four times larger — and would govern a much heavier section.

The conversions engineers actually need

Line loads travel between SI-metric, mixed-metric, and US-customary documents, so a handful of conversions come up constantly. The first one is so clean it is worth memorising.

  • kN/m ↔ N/mm: they are identical. 1 kN/m = 1 N/mm, exactly. A kilonewton is 1,000 N and a metre is 1,000 mm, and the two factors of 1,000 cancel: 1 kN/m = 1,000 N / 1,000 mm = 1 N/mm. This is enormously convenient — if you do a beam calculation in N and mm (as most structural software does internally), a load you wrote as 15 kN/m is simply 15 N/mm with no arithmetic at all. You can move between the two notations with the kN/m to N/mm converter but the factor is just 1.
  • kN/m → lb/ft (force per length): 1 kN/m ≈ 68.52 lbf/ft. To go to US-customary force-per-length you convert both the force and the length: 1 kN = 224.809 lbf and 1 m = 3.2808 ft, so 1 kN/m = 224.809 lbf ÷ 3.2808 ft = 68.52 lbf/ft. Our 15 kN/m design load is therefore about 1,028 lbf/ft.
  • kN/m → kgf/m: 1 kN/m ≈ 101.97 kgf/m. In older or gravitational-metric documents a line load may be given in kilogram-force per metre. Since 1 kgf = 9.80665 N, 1 kN/m = 1,000 N/m ÷ 9.80665 = 101.97 kgf/m.

Line load versus linear mass density: the lb/ft ↔ kg/m trap

Here is the conversion that trips people up, because it looks like the same thing and is not. Cables, ropes, pipes, and rolled-steel sections are catalogued by their linear mass density — their mass per unit length — in kg/m or lb/ft. A steel wire rope might be 4.4 kg/m; an AISC W14×90 beam is, by definition, 90 lb/ft. That lb/ft is a mass per length (force has not entered yet), and the relevant conversion is purely about mass and length:

  • 1 lb/ft = 1.488 kg/m (one pound-mass per foot equals 0.45359 kg ÷ 0.3048 m = 1.48816 kg/m), and inversely 1 kg/m = 0.672 lb/ft. The lb/ft to kg/m converter handles this linear-density pair.

Contrast that with the force-per-length conversion above: 1 kN/m ≈ 68.52 lbf/ft, where the imperial side is lb-force per foot (lbf/ft). Two superficially similar-looking “lb/ft” numbers — one a mass per length, one a force per length — differ by the factor g and by what they physically represent. The clean way to keep them apart:

  • kg/m and lb/ft are linear mass density — the property of a cable, pipe, rope, or steel section as it sits on a shelf. They live in the linear-density converter.
  • kN/m and lbf/ft are line loads (force per length) — what that object actually applies to the structure once gravity (or wind, or pre-tension) acts on it. The bridge between the two is multiplication by g ≈ 9.81 m/s².

Worked through: a W14×90 beam is 90 lb/ft = 133.9 kg/m of mass. Its self-weight line load is 133.9 kg/m × 9.81 m/s² ≈ 1,314 N/m ≈ 1.31 kN/m. The 90 lb/ft (mass) and the 1.31 kN/m (force) describe the same beam — one is what it is, the other is what it does to whatever holds it up. Confusing the two, or converting a mass density as though it were a load, drops or inserts a stray factor of about 9.81 and is one of the most common errors in this corner of engineering. When the underlying load is a force (snow, wind, equipment) it is already a force per length; only when the quantity is a mass per length (a catalogued cable or section weight) do you multiply by g to get the kN/m load.

Common mistakes to watch for

  • kN/m versus kN/m².The most frequent error: treating an area pressure (kN/m²) as if it were a line load (kN/m), or vice versa. They are different quantities separated by a length; always confirm whether a number is “per metre” or “per square metre” before it touches a beam.
  • Forgetting the tributary width.Floor and roof loads are given as kN/m² and must be multiplied by the beam’s tributary width (typically half-span to the next parallel member on each side) before they become a kN/m line load. Skipping this either drops the load entirely (if you forget) or mis-sizes it (if you guess the width).
  • Mixing mass-per-length with force-per-length. A catalogued lb/ft or kg/m is a massdensity; multiply by g to get the load it imposes. Don’t convert a mass density straight into kN/m, and don’t treat lbf/ft (force) and lb/ft (mass) as the same unit.
  • Dropping the L² in the moment. Mmax for a simply supported UDL is wL²/8, not wL/8 or wL²/4. Using the wrong divisor — or forgetting that L is squared — is an easy slip that scales the moment by a large factor.
  • Unit inconsistency at the end. Work consistently: if w is in kN/m and L in m, then wL is in kN and wL²/8 in kN·m. Slipping between m and mm mid-calculation is where many otherwise-correct beam checks go wrong; recall that 1 kN/m = 1 N/mm makes the N-mm system painless.

The takeaway

A kN/m line load is force spread along a length, and almost every beam calculation begins by assembling it from self-weight, tributary floor and roof loads (area load in kN/m² times tributary width in m), and wall, snow, and wind contributions. Once you have a uniform w in kN/m, a simply supported span gives reactions of wL/2 and a mid-span moment of wL²/8, while a cantilever gives wL and wL²/2 — and the L² term is the intuition to keep. The conversions worth holding in your head are the exact identity 1 kN/m = 1 N/mm, the force conversion 1 kN/m ≈ 68.52 lbf/ft, and, kept firmly separate, the linear-mass-density conversion 1 lb/ft = 1.488 kg/m for cables, pipes, and catalogued steel sections. Keep force-per-length and mass-per-length in different mental boxes, bridged only by gravity, and the whole subject stays clean. Run the 15 kN/m, 6 m example through the beam bending calculator and you should land on the same 45 kN reactions and 67.5 kN·m moment — a sign your load take-down and your arithmetic agree.