# The FROSIO calculation question, worked end-to-end

Source: https://coatmentor.com/blog/frosio-written-calculation-worked · Updated 2026-10-12

Unlike the AMPP CIP exams, the **FROSIO theory exam is open/written**, and it typically ends with a longer **paint-consumption calculation** that catches people out — not because the maths is hard, but because the *terms* get mixed up under time pressure. Here is the whole method, worked with a full example.

**The short answer:** [Theoretical spreading rate](https://coatmentor.com/glossary/#t-spreading-rate) = 10 × [volume solids](https://coatmentor.com/learn/volume-solids/) % ÷ DFT (µm). Wet film = DFT × (100 + thinner %) ÷ volume solids %. Practical spreading rate = theoretical rate × loss factor. Paint needed = area ÷ practical rate, rounded up to whole packs. Thinner changes the wet film you apply, not the amount of paint you order.

> **Note:** the method below (loss factor, consumption factor, the WFT formula) uses the same relationships paint manufacturers print on their technical data sheets (theoretical spreading rate from volume solids and DFT). The numbers below are an **original worked example**, not a copied exam question.

## The quantities you'll juggle

- **DFT** — [dry film thickness](https://coatmentor.com/learn/dft-measurement/), the spec target (µm).
- **WFT** — [wet film thickness](https://coatmentor.com/glossary/#t-wet-film-thickness), what you apply to *land* that DFT (µm).
- **VS** — volume solids of the product, % (the share that stays behind as film).
- **Thinner %** — how much thinner is added.
- **Loss factor** — the fraction of paint that actually ends up on the steel, after losses such as [overspray](https://coatmentor.com/glossary/#t-overspray), wastage and paint left in the equipment. Loss factor = (100 − loss%) / 100.
- **Consumption factor** — simply 1 / loss factor. (Mixing these two up is the single most common mistake.)
- **Theoretical spreading rate (TSR)** — how far 1 litre goes at the target DFT with zero losses (m²/L).
- **Practical spreading rate (PSR)** — TSR after losses.
- **Dead volume (DV)** — the dry paint that fills the valleys of the blast profile. It is added to the primer's quantity only; the other coats are not affected. The exam gives it per square metre, in ml/m² or L/m². Dead volume paint = area × DV × 100 ÷ (VS% × loss factor), in litres when DV is in L/m².

## The four formulas

1. **Theoretical spreading rate:** `TSR (m²/L) = 10 × VS% ÷ DFT(µm)`
2. **Wet film to apply:** `WFT = DFT × (100 + thinner%) ÷ VS%`
3. **Practical spreading rate:** `PSR = TSR × loss factor`
4. **Paint needed:** `Volume = Area ÷ PSR`, then **round up to the supplier's pack size** (commonly 20 L pails, as in the worked example below).

## Worked example

> Apply one coat to **600 m²** of steel. Spec DFT **200 µm**. Product volume solids **70%**, thinned **10%**. Allow **30%** total losses.

### Step 1 — Theoretical spreading rate

  TSR = 10 × 70 ÷ 200 = 3.5 m²/L

One litre covers 3.5 m² at 200 µm — if nothing were lost.

### Step 2 — Wet film thickness to apply

  WFT = 200 × (100 + 10) ÷ 70 = 200 × 110 ÷ 70 ≈ 314 µm

You set your wet-film comb to land ~314 µm wet so that, after the solvent (and the 10% thinner) flash off, you're left with 200 µm dry.

### Step 3 — Practical spreading rate

  Loss factor = (100 − 30) ÷ 100 = 0.70
PSR = 3.5 × 0.70 = 2.45 m²/L

### Step 4 — Paint needed

  Volume = 600 ÷ 2.45 ≈ 244.9 L  →  round up to pack size  →  260 L (13 × 20 L)

### Cross-check with the consumption factor

  Consumption factor = 1 ÷ 0.70 ≈ 1.43
Theoretical volume = 600 ÷ 3.5 = 171.4 L
Practical volume   = 171.4 × 1.43 ≈ 244.9 L  ✓ — same answer, both routes.

## The trap almost everyone falls into

**Thinner changes your WFT, not your order quantity.** Notice that the 10% thinning appears in Step 2 (the wet film you apply) but **nowhere** in the paint volume you buy. That's because consumption is driven by *solids* — the dry film you need — and thinner adds no solids. If you inflate the procurement figure by the thinning percentage, you'll over-order every time.

The other classic slip is **loss factor vs consumption factor**: you *multiply* theoretical spreading rate by the loss factor (a number below 1), or you *multiply* theoretical volume by the consumption factor (a number above 1). Reach for the wrong one and your answer lands in the wrong direction.

## How to actually get fast at this

The only cure is reps with the method, not re-reading it. Work several examples end-to-end until the four steps are automatic and you can spot, mid-question, which factor goes where — and remember to do it per coat and sum for a multi-coat system.

Related guides: [What is the FROSIO inspector certification?](https://coatmentor.com/blog/what-is-the-frosio-exam) · [The ISO 12944 guide](https://coatmentor.com/blog/iso-12944-guide) · [FROSIO vs AMPP CIP](https://coatmentor.com/blog/frosio-vs-ampp-cip) · [WFT ↔ DFT formula and calculator](https://coatmentor.com/blog/wft-dft-formula-calculator).

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