LiDAR building volume as a rebuild-cost input

Why footprint times storeys misstates a house

The size input to a house's rebuild cost is usually a guess. Cadastres record a plot and a building footprint, rarely a floor count and never a volume; the owner remembers the living area, which is a different quantity again; the insurer's form asks for a third. The common shortcut, footprint × storeys, fails in four ways. It ignores the roof: a habitable attic under a pitched roof is neither a full storey nor nothing, and an appraiser counts it at about 0.6 of the footprint. It ignores the basement, which about 45 percent of houses in one sample of expert appraisals have. It depends on a storey count that is itself estimated, and a wrong count is a 50 or 33 percent error. And it uses the wrong footprint: a cadastral wall footprint is about 0.87 of the roof extent seen from above, so a footprint read off an aerial image over-states the building by the eaves overhang.

The errors compound with the carriers' area definitions. When one comparison page sent the same gross all-storey area to nine household calculators, a 137 m2 footprint house with two scanned storeys was priced as a 550 m2 building by a carrier that expected the footprint plus a storey count, and as a 275 m2 building by carriers that expected net area; the house quotes came out about 3.5 times a 65 m2 flat, where real quotes put such a house at 1.0 to 1.4 times. The first job of a measured volume is therefore not precision for its own sake but a defined quantity that can be converted correctly to whatever area basis each policy uses. The rebuild-cost guide lists those bases.

Airborne LiDAR: point cloud, terrain model, surface model

Airborne laser scanning fires pulses from an aircraft and records the returns, giving a cloud of classified points (ground, building, vegetation). Two rasters are derived from it and a third from their difference. National programs publish them under open licenses in a growing number of countries; a 2021 JRC inventory counted 18 of 32 European countries fully covered by open LiDAR, nine partially and five without data.

National program figures from the Slovak flood-risk data sources guide; derivations from the Bytero Recover method.

From a footprint and a height to enclosed volume

The statutory size quantity for a house in Slovak appraisal practice is the enclosed volume (obostavaný priestor) under standard STN 73 4055: the volume over the built-up area, roof included, eaves overhang excluded. With a full nDSM it is an integral: sum the height above ground over every cell inside the wall footprint. With only a footprint and a ridge height it is a geometric model, and the choice of model is the whole error budget. The naive prism, footprint × ridge height, treats the attic as a full box and over-counts: against laser-measured volumes over 1,473 houses it ran a median 1.16 times the truth.

A box-plus-wedge model fixes that. Count floors as round((ridge − 2.5 m) / 3.2 m), where 2.5 m is the rise of the roof above the top ceiling and 3.2 m a structural storey including the slab; set the eave at floors × 3.2 m; take the walls as a box to the eave and the roof as a wedge, half the box from eave to ridge. Volume = footprint × eave + footprint × rise × 0.5. On the same 1,473 houses that lands at a median 1.02 times the measured volume with a 14 percent median absolute error and no bias, and an independent check on 91 houses against a roof surface model from a different provider agreed at 1.01 with 23 percent error. The floor count was within one storey on every house of a 60-house reference set and exact on 84 percent.

Worked through: a 137 m2 wall footprint with an 8.0 m ridge. Floors = round((8.0 − 2.5) / 3.2) = round(1.72) = 2; eave 6.4 m; rise 1.6 m. Volume = 137 × 6.4 + 137 × 1.6 × 0.5 = 876.8 + 109.6 = 986 m3. The prism would say 137 × 8.0 = 1,096 m3, 11 percent more. A hip roof on the same house, factor 0.42, gives 969 m3.

Floor area from volume, on the carrier's definition

Appraisers and carriers price per square meter, not per cubic meter, so the volume model's real output is a set of areas. From footprint, floor count and eave height every area definition in use can be derived, and each should be reported with its label so that a carrier's form receives the quantity it expects.

Derivations from the Bytero Recover method; ratios are rules of thumb for a masonry house.

Cost per cubic meter versus cost per square meter

A cubic-meter rate looks like the natural partner of a measured volume, and it is the wrong pricing basis. Expert appraisals of houses under decree 492/2004 price per square meter of built-up area per storey, times a chain of coefficients, and in a harvest of about 15 real appraisals none priced by volume. One engine that started with a per-cubic-meter rate found it about 2.5 times too high against those appraisals and retired it. The current basis is a unit cost of 160 EUR per m2 of built-up area at 1996 prices, lifted by the 1Q/2025 price-level coefficient of 3.954 to about 633 EUR/m2 and, after material and location coefficients, to an effective 683 EUR/m2, against a median of about 682 EUR/m2 in the real appraisals. Because that sample is small, the cost is honestly ±25 percent, while the geometry behind it is ±14 percent: the volume is the tight number, the unit cost the loose one.

For comparison, the flat basis in the same decree is a unit cost of 325.30 EUR per m2 of floor area at 1996 prices, about 1,286 EUR/m2 at the 2025 price level before material and location coefficients. A 274 m2 gross floor area at 683 EUR/m2 puts the example house at roughly 187,000 EUR of reconstruction value above ground. The cubic meter still has a job: it is the statutory geometric quantity reported alongside the cost, the cross-check that catches a wrong storey count, and the input a surveyor recognizes.

Roof shape

The wedge factor assumes a gable. Other roofs enclose a different share of the box between eave and ridge, and the shape can be read from the roof surface where a surface model or a roof-segment service is available: cluster the pitched segments by azimuth (merging within 45 degrees, counting a direction only when it holds at least 12 percent of the pitched area) and count the directions.

Factors and detection rule from the Bytero roof-form classifier. A flat verdict is rejected where the scan shows more than 1.2 m of rise.

Error sources and partial coverage

A measured volume is still a model of a building, and each of its inputs fails in a known direction. Coverage is the other limit: even where a national program exists, the newest products (a 0.5 m surface model, the second scanning cycle) are published for part of a country's territory at a time, and the rest falls back to the older raster or to the single-height building layer.

Directions and magnitudes from the Bytero Recover method.

Feeding the sum insured

The path from a scan to a policy figure, in the order the checks should run.

1. 1

   Locate the building

   Pick the footprint polygon that contains the address point, not the nearest centroid; an address point can sit in a small front structure while the house stands 9 m away, so flag any larger building within 15 m.

2. 2

   Read height and footprint

   Ridge height and wall footprint from the building layer, or the nDSM integral over the wall footprint where a surface model is published; record which one was used and the scan date.

3. 3

   Derive storeys, roof form and volume

   Floors from the ridge with the roof allowance, eave from the floors, roof factor from the detected form, volume from the box plus wedge.

4. 4

   Convert to the carrier's area basis

   Gross, net, footprint plus storeys or living area, each with its label, plus a cellar term where the owner or an appraisal reports one.

5. 5

   Price and flag

   Unit cost per m2 of built-up area per storey times the decree coefficients for price level, material and location; report the ±25 % cost band and the ±14 % geometry band separately, and mark the sum as above-ground only.

6. 6

   Index and keep the evidence

   Store footprint, height, floors, roof form, scan date and coefficients with the policy, so the sum can be recomputed after the next index letter or the next scan cycle.

In practice

A measured volume turns the least reliable input of a house policy into the most reliable one and leaves the unit cost as the remaining uncertainty. Bytero derives footprint, storeys, height, enclosed volume and the reconstruction value for a house from the national LiDAR building layer, with the laser validation quoted on this page, through Bytero Recover; availability by market is on the coverage page.

Questions