Size Reduction Energy Calculator
Grinding a material with a work index of 13 kWh/t from 10 mm to 1 mm takes 2.81096 kWh/t.
Limestone about 11–13, quartz 13–14, granite 15–17.
2.81096095821889 kWh/t
Full answer, then cut to fewer decimals (not rounded):
- 2.81096095821889 kWh/t
- 2.8109609582188 kWh/t
- 2.810960958218 kWh/t
- 2.81096095821 kWh/t
- 2.8109609582 kWh/t
- 2.810960958 kWh/t
- 2.81096095 kWh/t
- 2.8109609 kWh/t
- 2.810960 kWh/t
- 2.81096 kWh/t
- 2.8109 kWh/t
- 2.810 kWh/t
- 2.81 kWh/t
- 2.8 kWh/t
- Power required
- 28.10960958 kW
- Reduction ratio F/P
- 10
Step-by-step solution
- W = 10 W_i (1/√P − 1/√F) with sizes in µm
- W = 10 × 13 × (1/√1000 − 1/√10000) = 2.810960958 kWh/t
Size Reduction Energy Formula
W = 10 W_i (1/√P₈₀ − 1/√F₈₀)
Rittinger E ∝ 1/L₂ − 1/L₁; Kick E ∝ ln(L₁/L₂); sizes in µm
Worked Example
Grinding from 10 mm to 1 mm with W_i = 13 kWh/t:
- W = 10 W_i (1/√P − 1/√F) with sizes in µm
- W = 10 × 13 × (1/√1000 − 1/√10000) = 2.810960958 kWh/t
Reduction ratio F/P: 10
GATE tip
In “scale” questions, take the ratio of the same law for both reductions: the constant cancels.
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Minimum Fluidization Velocity Calculator
Re_mf = √(33.7² + 0.0408 Ar) − 33.7
Ar = d_p³ρ_f(ρ_p − ρ_f)g/μ², U_mf = Re_mf μ/(ρ_f d_p)
Example: 500 µm sand (2650 kg/m³) fluidized by air: Minimum fluidization velocity U_mf = 0.198901 m/s.
Frequently asked questions
Which law applies when?
Kick suits coarse crushing, Rittinger fine grinding, and Bond the intermediate range of most mills.
What do F₈₀ and P₈₀ mean?
The sizes through which 80 % of the feed and product pass.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Size Reduction Energy Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/size-reduction-energy-calculator/
IEEE
Scientific Converters, "Size Reduction Energy Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/size-reduction-energy-calculator/