Calculation Methodology

One internal base unit

Every measurement you type is converted into metres before anything else happens. Volumes are then held in cubic metres and masses in kilograms. Mixing units inside a calculation is the single most common source of wrong answers, so the calculators never do it: the unit you chose only affects how the number gets into the base unit, and how results are printed back out.

Length conversions

• 1 millimetre = 0.001 m
• 1 centimetre = 0.01 m
• 1 inch = 0.0254 m exactly
• 1 foot = 0.3048 m exactly

Volume conversions

• 1 litre = 0.001 m³
• 1 cubic foot = 0.028316846592 m³ exactly
• 1 cubic yard = 0.764554857984 m³ exactly

Mass conversion

• 1 pound = 0.45359237 kg exactly

The inch, foot, cubic foot, cubic yard and pound factors above are exact definitions rather than approximations, so converting from imperial to metric and back returns the original number.

Volume formulas

• Rectangular slab, path or footing: length × width × depth.
• Circular slab: π × (diameter ÷ 2)² × depth.
• Cylindrical column: π × (diameter ÷ 2)² × height. Identical maths to a circular slab; only the language differs.
• Square or rectangular post hole: width × length × depth, minus post displacement.
• Round post hole: π × (diameter ÷ 2)² × depth, minus post displacement.

π is JavaScript's Math.PI, accurate to about fifteen decimal places — far beyond the accuracy of any site measurement.

Multiple sections and identical counts

Each section is calculated on its own and multiplied by its quantity. The section totals are then added together. Nothing is averaged, because averaging different thicknesses produces a figure that matches no part of the actual pour.

Waste

Waste is applied once, to the combined net volume, after every section has been added: total = net × (1 + waste ÷ 100). Applying it per section would compound rounding and produce a slightly different figure depending on how you split the job up, which would be arbitrary.

The offered values — 0%, 5%, 10% and 15% — are common allowances, not requirements, and the custom field accepts anything you prefer. Waste is a judgement about your site, not a property of concrete.

Bag quantities and rounding

Bags = required volume ÷ the manufacturer's stated wet yield per bag. That figure is then rounded up to the next whole bag, because bags are not sold in fractions. A tiny floating-point tolerance is applied before rounding so that a result which is mathematically exactly 10 bags does not become 11.

The exact, unrounded bag figure is always displayed alongside the purchase quantity so you can see how close you are to the next bag.

Why bag weight does not determine yield

A bag's weight tells you how much dry material it holds, not how much wet concrete it makes. Yield depends on aggregate size, density, the mix design and how much water is added. Two bags of the same weight from different manufacturers can produce noticeably different volumes. For that reason the calculators only offer a yield where a manufacturer publishes one, and you can always enter the figure printed on the bag you are actually buying, in litres, cubic metres, cubic feet or cubic yards. It is converted internally.

Estimated standard yield versus manufacturer-stated yield

For 40, 50, 60, 80 and 90 lb bags of ready-to-use pre-mixed concrete, the calculators offer an estimated standard yield taken from the QUIKRETE Concrete Mix (Product No. 1101) data sheet: 0.30, 0.375, 0.45, 0.60 and 0.675 cubic feet per bag. Any bag count based on these figures is labelled as an estimate, because other products of the same weight can yield differently. For 20 kg bags there is one UK reference estimate: Tarmac states that a 20 kg bag of Blue Circle Multi-Purpose Ready-to-Use Concrete produces around 0.01 m³ (10 litres). That figure belongs to that product only and is not a universal yield for every 20 kg bag. No estimate is offered for 25, 30 or 40 kg bags or custom weights, because no published figure could be sourced for them; there you must enter the manufacturer-stated yield.

A yield you type in always replaces the estimate and is never overwritten by other settings. If you change the bag weight, a yield you typed for the previous bag is cleared and you are told so, because it belongs to a different product. The yield actually used is shown in the results. These figures are for pre-mixed concrete, not pure cement powder, and no extra waste is added beyond the percentage you choose.

Density and sub-base mass

Where a sub-base mass is shown it is simply volume × the density you entered. No default density is assumed, because aggregate density varies by material, source and moisture content. If you do not have a figure from your supplier, leave it blank and work in volume only.

Loose versus compacted sub-base

Granular material shrinks when compacted, so the volume you need to buy is larger than the compacted volume you want in the ground. Compacted volume = area × finished depth. Loose volume = compacted volume × compaction factor, and the delivery volume then adds waste: compacted × compaction factor × (1 + waste ÷ 100). The compaction factor is yours to set from supplier information.

MOT Type 1 weight and bulk bags

The MOT Type 1 calculator converts volume to weight with the density type you choose, so compaction is never counted twice: compacted density × compacted volume × (1 + waste), or loose density × loose delivery volume. Its starting values (2,100 kg/m³ compacted, 1,800 kg/m³ loose, a 1.2 compaction factor and an 850 kg bag) are editable estimates, not universal figures. Imperial densities are converted from lb/ft³ to kg/m³ first; tonnes are 1,000 kg and US tons 2,000 lb. Bulk bags = weight ÷ bag capacity, rounded up only for the purchase count.

Post displacement

Displaced volume = post cross-section × embedded depth, where cross-section is width × depth for a rectangular post and π × radius² for a round one. Two safeguards apply: the embedded depth is capped at the hole depth (less any concrete poured beneath the post), and the displaced volume is capped at the hole volume, so a result can never go negative. If the post would fill the hole entirely, the calculator says so rather than printing zero.

Ready-mix minimum orders

If you enter a supplier minimum and your calculated volume is below it, the order quantity is raised to the minimum and the difference is reported separately. Your calculated volume is never silently overwritten.

Currency handling

Costs are volume or bag count multiplied by the price you type in. There is no price database, no market average and no exchange-rate conversion. The currency symbol is a display label attached to your own numbers; changing region changes the symbol, never the arithmetic.

Precision and rounding for display

All intermediate maths uses full double-precision floating point. Rounding happens only when a number is printed. That means the total of the displayed section volumes may differ from the displayed total by a small amount in the last decimal place — the total is correct and the parts are rounded, not the other way round.

Why results are estimates

Sub-grade is never perfectly flat, formwork moves, over-dig happens, some concrete is left in the barrow and stated yields are nominal. Even a perfectly executed calculation meets an imperfect site. Treat every figure here as a well-informed starting point for a conversation with your supplier, not as a guaranteed quantity.

How the calculations are tested

The conversion, volume, waste, bag, minimum-order and post-displacement functions are covered by an automated test suite that runs against known values in both metric and imperial, including round-trip conversions, zero and negative inputs, NaN and Infinity, displacement larger than the hole, and bag counts that land exactly on a whole number. The tests exercise the same functions the pages use, so a page cannot drift away from the tested behaviour.