Drying Time Calculator (constant & falling rate)

Understanding the drying time calculator — concept and principle

Batch dryers for foods, pharmaceuticals, minerals and timber are sized from a drying curve: a period at constant rate followed by a period where the rate falls as the solid dries out. This calculator uses the textbook model of those two periods to estimate the time needed to dry a batch from an initial to a final moisture content.

Removing the last 0.15 kg/kg takes almost as long as the first 0.3 because the rate keeps slowing.

How it is calculated

Constant-rate time: t₁ = mₛ ÷ (A × Rc) × (X₁ − Xc).
Falling-rate time (rate linear in moisture): t₂ = mₛ ÷ (A × Rc) × (Xc − Xe) × ln[(Xc − Xe) ÷ (X₂ − Xe)].
Total time: t = t₁ + t₂, in hours.

mₛ is the bone-dry solid mass (kg), A the drying surface (m²), Rc the constant drying rate (kg water per m² per hour), and X₁, Xc, X₂ and Xe the initial, critical, final and equilibrium moisture contents in kg water per kg dry solid.

The principle

While the surface stays wet, the solid behaves like a pool of free water: the drying rate is set only by how fast heat reaches the surface and vapour leaves it, so it stays constant at Rc. Once moisture falls below the critical value Xc, water must move from inside the solid to the surface and the rate drops. The simplest model assumes the rate falls in a straight line, R = Rc (X − Xe)/(Xc − Xe), reaching zero at the equilibrium moisture Xe, below which the air cannot dry the solid. Integrating dt = −mₛ dX/(A R) over each period gives the two formulas.

Worked example

Defaults: mₛ = 100 kg, A = 10 m², X₁ = 0.5, Xc = 0.2, X₂ = 0.05, Xe = 0.01, Rc = 1.5 kg/m²·h.
mₛ ÷ (A × Rc) = 100 ÷ 15 = 6.667 h per unit of moisture.
Constant rate: 6.667 × (0.5 − 0.2) = 2 h.
Falling rate: 6.667 × 0.19 × ln(0.19 ÷ 0.04) = 1.2667 × 1.5581 = 1.97 h.
Total: 2 + 1.974 = 3.97 h.

Each point is the calculator re-run with only “Drying area (m²)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Drying area (m²)	Constant-rate time (h)
2.5	8
5	4
7.5	2.666666667
10	2
12.5	1.6
15	1.333333333
20	1

How to read the result

Here the last 0.15 kg/kg of moisture takes as long as the first 0.30, a typical pattern: the falling-rate period dominates when you dry close to equilibrium. Halving X₂ − Xe adds a fixed slice of time because of the logarithm, so specifying a drier product than necessary is costly. Hotter or faster air raises Rc and shortens both periods.

Common mistakes

Entering wet-basis moisture; convert with X = w/(1 − w), so 20% wet basis is 0.25 kg/kg dry basis.
Setting X₂ equal to or below Xe, which cannot be reached and makes the logarithm undefined.
Taking Rc and Xc from another material or other air conditions; both must come from a drying test.

Keep in mind: The linear falling-rate model is an approximation; many materials show curved or two-stage falling-rate periods, and shrinkage or case hardening changes the behaviour. Use measured drying curves for equipment design.

Frequently asked questions

What is the critical moisture content?

The moisture at which the surface stops being fully wet and the rate begins to fall. It depends on the material, layer thickness and drying conditions.

What is equilibrium moisture?

The moisture the solid would reach after infinite time in air of the given temperature and humidity.

Why does mass appear as dry solid?

Moisture contents are expressed per kg of dry solid, which does not change during drying.

Sources: Geankoplis, C. J. Transport Processes and Separation Process Principles. Prentice Hall. · McCabe, W. L., Smith, J. C. & Harriott, P. Unit Operations of Chemical Engineering. McGraw-Hill.

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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