Parallel Plate Torque to Viscosity Calculator

Turn measured torque into viscosity with confidence quickly. Choose units, enter geometry, view shear rates. Export results for reports, audits, and repeatable testing easily.

Inputs
Use steady torque at the chosen speed.
Use the effective radius filled by the sample.
Smaller gaps increase shear rate for the same speed.
Converted internally to angular speed (rad/s).
Record conditions to improve reproducibility.
Saved in exports for traceability.
Reset

Formula used

For a Newtonian fluid sheared between two parallel circular plates of radius R, separated by a gap h, with angular speed ω, the ideal torque is:

T = (π η ω R⁴) / (2 h)

Solving for dynamic viscosity η:

η = (2 h T) / (π ω R⁴)

Extra outputs: rim shear rate γ̇R = ωR/h, rim shear stress τR = 2T/(πR³), and power P = Tω.

How to use this calculator

  1. Measure steady torque at a known rotational speed.
  2. Enter the effective plate radius filled with sample.
  3. Enter the plate gap used during the run.
  4. Select correct units for every input.
  5. Click Calculate to view viscosity above the form.
  6. Use CSV or PDF export for lab notes and reports.

Example data table

Torque Radius Gap Speed Estimated viscosity
0.012 N·m 25 mm 1 mm 30 rpm 0.0391 Pa·s (39.1 mPa·s)
0.006 N·m 20 mm 0.8 mm 60 rpm 0.0153 Pa·s (15.3 mPa·s)
0.025 N·m 30 mm 1.5 mm 10 rpm 0.1180 Pa·s (118.0 mPa·s)
Examples assume ideal Newtonian behavior and full plate fill.

Technical article

1) Why torque reveals viscosity

In a parallel-plate test, the rotating plate drags fluid layers across a controlled gap. The instrument reads torque, which is the integrated resistance to shear over the disk area. For an ideal Newtonian sample, higher viscosity produces a proportionally higher torque at the same speed, radius, and gap.

2) What the calculator actually computes

The calculator converts your entered torque and speed into SI units, then applies the closed-form disk relation to solve for dynamic viscosity (Pa·s). It also reports rim shear rate, rim shear stress, and mechanical power. These extra outputs help compare tests conducted with different geometries and operating points.

3) Geometry sensitivity and the R⁴ effect

Radius dominates the result: viscosity scales with 1/R⁴. A small radius error can strongly shift the estimate. For example, if the true radius is 25 mm but 24.5 mm is entered, the R⁴ term changes by about 8%, pushing viscosity upward by a similar fraction. Measure the effective filled radius carefully.

4) Gap control and shear-rate targeting

The gap sets the shear field thickness and directly affects rim shear rate: γ̇R = ωR/h. With R = 25 mm and h = 1 mm, a speed of 30 rpm gives ω ≈ 3.1416 rad/s and γ̇R ≈ 78.5 s⁻¹. Decreasing the gap to 0.5 mm doubles shear rate without changing speed.

5) Interpreting shear stress and power

Rim shear stress (τR) provides a quick check against material limits and slip risk. Power (P = Tω) indicates dissipated energy and potential heating for viscous samples. If power rises while temperature is uncontrolled, viscosity may drift during the run, especially for polymer melts and oils.

6) Typical viscosity scales and units

Many fluids are conveniently discussed in mPa·s (cP). Water near room temperature is about 1 mPa·s, light oils often fall between 10–200 mPa·s, and concentrated syrups can exceed 1,000 mPa·s. This calculator reports Pa·s and mPa·s side-by-side to reduce conversion mistakes.

7) Assumptions and when results shift

The closed-form expression assumes Newtonian behavior, uniform gap, full plate fill, and no slip. Non-Newtonian samples can show viscosity that depends on shear rate, so repeat calculations at multiple speeds. Edge effects, partial filling, or plate slip usually reduce measured torque, biasing viscosity low.

8) Practical workflow for reproducible tests

Record temperature, plate type, surface condition, and sample loading notes. Run at least three speeds and confirm torque stability. If you change radius, gap, or speed, use rim shear rate to compare like-for-like conditions. Finally, export CSV or PDF to archive inputs and computed outputs alongside instrument files.

FAQs

1) Is the viscosity here dynamic or kinematic?

This calculator outputs dynamic viscosity (Pa·s, mPa·s/cP). Kinematic viscosity (m²/s) requires density: ν = η/ρ.

2) Can I use rpm or rad/s for speed?

Yes. Select rpm or rad/s. The calculator converts to angular speed in rad/s before computing viscosity and shear-rate outputs.

3) What if my sample is shear-thinning?

Compute viscosity at multiple speeds and compare the reported rim shear rate. A decreasing viscosity with increasing shear rate suggests shear-thinning behavior.

4) Why is radius so important?

The torque model contains R⁴. A small radius measurement error can significantly change viscosity. Use the effective filled radius, not just the plate diameter.

5) How do I reduce slip errors?

Use roughened plates, appropriate normal force (if your instrument supports it), and avoid very low stresses. Slip often appears as unexpectedly low torque at higher speeds.

6) Does temperature matter?

Strongly. Many fluids change viscosity by several percent per °C. Enter temperature for documentation and keep it controlled during runs for consistent results.

7) What is the rim shear rate used for?

It provides a comparable operating point across tests. Matching rim shear rate helps compare results even when radius, gap, or speed differ.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.