Dissolution Rate Calculator

Calculate drug or crystal dissolution rate using the Noyes-Whitney equation.

Diffusion coefficient D (cm²/s) (cm²/s)

Surface area A (cm²) (cm²)

Diffusion layer thickness h (cm) (cm)

Typical: 0.003 cm = 30 μm

Saturation solubility Cs (mg/mL) (mg/mL)

Bulk concentration Cb (mg/mL) (mg/mL)

0 = sink conditions

Please check your inputs and try again.

What Controls Dissolution Rate

The Noyes–Whitney equation describes dissolution as diffusion across a thin stagnant layer at the solid surface. Every term in it is a lever formulators can pull.

dC/dt = (D × A × (C_s − C_b)) / h

Term	Meaning	How it is changed
D	Diffusion coefficient	Fixed by molecule and medium
A	Surface area	Micronisation, nanocrystals — the main lever
C_s	Saturation solubility	Salt forms, amorphous solids, co-crystals
C_b	Bulk concentration	Sink conditions keep this near zero
h	Diffusion layer thickness	Agitation reduces it

Surface area is the dominant practical lever. Because area scales with the inverse of particle diameter, reducing particle size tenfold increases surface area tenfold and dissolution rate with it. This is why micronisation is the standard first response to a poorly dissolving drug.

Sink Conditions and the BCS

When C_b stays well below C_s — conventionally under 10% — the driving force is essentially constant and dissolution proceeds at a steady rate. These sink conditions are required for meaningful dissolution testing, and they approximate the gut, where absorption continuously removes dissolved drug.

BCS class	Solubility	Permeability	Rate-limiting step
I	High	High	Gastric emptying
II	Low	High	Dissolution
III	High	Low	Permeation
IV	Low	Low	Both — problematic

Class II drugs are where this equation earns its keep: they are absorbed well once dissolved, so dissolution is the sole bottleneck and formulation can solve it. A large share of modern drug candidates fall into this class.

Worked Examples

Example 1: Poorly soluble drug: D=1e-5, A=10cm², h=0.003, Cs=0.01mg/mL

rate=1e-5×10×0.01/0.003

Result: rate=3.3×10⁻⁴ mg/s — very slow dissolution

BCS Class II drug: dissolution rate limited

Example 2: After micronization 10× more surface area: A=100cm²

rate=3.3×10⁻³ mg/s

Result: 10× faster dissolution

Particle size reduction is key formulation strategy

Example 3: Amorphous form

Crystalline C_s = 0.01 mg/mL, amorphous = 0.05 mg/mL

Result: Fivefold rate increase

Amorphous solids lack crystal lattice energy so dissolve faster, but they are thermodynamically unstable and tend to recrystallise on storage.

Example 4: Why BCS II matters

Low solubility, high permeability

Result: Dissolution is the only bottleneck

Once dissolved the drug is absorbed efficiently. Formulation that improves dissolution directly improves bioavailability, which is why so much effort goes into this class.

Common Mistakes

⚠️

Assuming smaller particles always solve the problem

Micronisation increases surface area but can cause aggregation, which reduces effective area. Nanosuspensions need stabilisers to prevent this.

⚠️

Testing without sink conditions

If bulk concentration approaches saturation, the driving force collapses and the measured rate underestimates in vivo behaviour.

⚠️

Confusing solubility with dissolution rate

Solubility is the equilibrium endpoint; rate is how fast it is approached. A poorly soluble drug can dissolve quickly if finely divided.

⚠️

Ignoring the diffusion layer

Agitation reduces h and raises rate. Dissolution testing must specify stirring speed, or results are not comparable.

Frequently Asked Questions

BCS classification and dissolution?

Class I (high sol, high perm): no dissolution issues. Class II (low sol, high perm): dissolution rate limited — formulation critical. Class III (high sol, low perm): permeability limited. Class IV: both problems. 40% of drugs are BCS Class II.

Formulation strategies for poor dissolution?

1. Reduce particle size (micronization, nanonization). 2. Form more soluble salts or cocrystals. 3. Amorphous solid dispersions (higher Cs). 4. Lipid formulations (self-emulsifying). 5. Cyclodextrin complexation. 6. Hot melt extrusion.

What is the main way to speed up dissolution?

Increasing surface area through particle size reduction. Area scales inversely with particle diameter, so micronisation gives a proportional rate increase.

What are sink conditions?

Bulk concentration kept below about 10% of saturation, so the concentration gradient stays roughly constant. They are required for valid dissolution testing.

What is BCS Class II?

Low solubility with high permeability. Dissolution is the rate-limiting step for absorption, so formulation improvements translate directly into bioavailability gains.

Why do amorphous forms dissolve faster?

They lack crystal lattice energy, giving higher apparent solubility. The drawback is thermodynamic instability — they tend to recrystallise during storage.

Formula Explorer connections

Interpretation: This formula connects concentration, time, temperature or transport to the speed of a chemical process. Assumption: The reaction order and mechanism must match the model. Temperature, catalyst, mixing and mass-transfer limitations can alter the observed rate.

First Order Kinetics Calculator →Half-Life Calculator (Chemistry) →Integrated Rate Law Calculator →Chemistry Formula Explorer →