Vacuum Pad Lifting Force Calculator
Vacuum pad lifting force (N, kgf) from pad diameter, vacuum and safety factor; vacuum or pad size for a load; pipe volume and response time (SMC).
Formulas (SMC)
- Lifting force W (N) = P (kPa) × S (cm²) × 0.1 × 1/t
- S = π/4 × (pad diameter in cm)², t ≥ 4 horizontal, ≥ 8 vertical
- Vacuum needed P = W × t ÷ (S × 0.1)
- Pipe volume V (L) = π/4 × D (mm)² × L (m) ÷ 1000
- Average suction flow Q = V × 60 ÷ T1 + QL, ejector max. suction flow = (2–3) × Q
- Response time T1 = V × 60 ÷ Q, T2 = 3 × T1, Q = smaller of Q1 and Q2
- Q1 = ejector max. suction flow × (1/2–1/3), Q2 = C × 55.5, leakage QL = 55.5 × CL
Lifting force by pad diameter (N, calculated)
| Pad | Area cm² | −60 kPa theoretical | −60 kPa horizontal (÷4) | −60 kPa vertical (÷8) | −80 kPa theoretical |
|---|---|---|---|---|---|
| ø10 | 0.785 | 4.71 | 1.18 | 0.589 | 6.28 |
| ø20 | 3.14 | 18.8 | 4.71 | 2.36 | 25.1 |
| ø32 | 8.04 | 48.3 | 12.1 | 6.03 | 64.3 |
| ø40 | 12.6 | 75.4 | 18.8 | 9.42 | 101 |
| ø50 | 19.6 | 118 | 29.5 | 14.7 | 157 |
| ø63 | 31.2 | 187 | 46.8 | 23.4 | 249 |
| ø80 | 50.3 | 302 | 75.4 | 37.7 | 402 |
| ø100 | 78.5 | 471 | 118 | 58.9 | 628 |
SMC's theoretical lifting force table uses the same formula but truncates or rounds the last digit (e.g. ø40 at −60 kPa: 75 N), so the last digit may differ from this table. Tests check that this calculator matches SMC's table within one last digit.
SMC selection example (checked by tests to give the same values)
- A 1 g semiconductor chip (0.0098 N) lifted horizontally by one ø4 pad (0.13 cm²), safety factor 4: P = 0.0098 × 4 ÷ (0.13 × 0.1) = 3.0 kPa → −3.0 kPa or more lifts it.
- 2 mm ID × 1 m pipe: V = π/4 × 2² × 1 ÷ 1000 = 0.0031 L. For 300 ms, Q = 0.0031 × 60 ÷ 0.3 = 0.62 L/min, so the ejector's max. suction flow should be 1.24–1.86 L/min or more.
- A 5 L/min ejector: Q1 = 5 × 1/3 ≈ 1.7; pipe C = 0.22 → Q2 = 12.2 L/min. With the smaller 1.7, T1 = 0.0031 × 60 ÷ 1.7 = 0.109 s (109 ms).
How to read it
- Doubling the vacuum doubles the force; doubling the pad diameter quadruples it. SMC notes that excessive vacuum wears pads faster and slows response, so match the force with pad size and count instead.
- Theoretical force is a static value. Acceleration, air flow and impact while moving, plus the side forces and moments pads resist poorly, are covered by the safety factor — hence 4 horizontal and 8 vertical.
- Porous or rough workpieces leak air and lower the vacuum. Calculate with the lowered vacuum, and add the leak as QL.
- An ejector's average suction flow is 1/2–1/3 of its maximum, so response time comes out as a range. Designing to the slower end (1/3) leaves margin.
FAQ
What is the vacuum pad lifting force formula?
SMC's formula is W (N) = P (kPa) × S (cm²) × 0.1 × 1/t. A ø40 pad (12.57 cm²) at −60 kPa has a theoretical force of 75.4 N; divided by a horizontal safety factor of 4, 18.8 N (about 1.9 kg).
What safety factor should I use?
SMC gives 4 or more for horizontal lifting (pad facing down) and 8 or more for vertical lifting (gripping a side face), and says vertical lifting should be avoided where possible.
Where does −60 kPa come from?
SMC says the vacuum with an ejector is about −60 kPa as a guide. Use a value below the stable vacuum after adsorption.
How do I calculate adsorption (response) time?
T1 = pipe volume V × 60 ÷ average suction flow Q gives the time to 63 % of the final vacuum; 95 % takes three times that. Longer, larger pipes mean more volume and a slower response.
For the force of the cylinder moving the pad, use the Pneumatic Cylinder Force Calculator. For the compressed air used by cylinders, use the Pneumatic Cylinder Air Consumption Calculator. For how to choose pads and an ejector, see the guide Vacuum pad lifting force and choosing an ejector.
Basis
Formulas and examples are from SMC's «Vacuum Equipment Model Selection» (PDFs on SMC's official site) — 4-P0878-883 (p.878 example; p.880 lifting force formula, safety factors and theoretical lifting force table), 6-4-p0033-vacuum (A33 §3 ejector flow formulas, §4 leakage), 6-4-p0034-vacuum (A34 §5 response time formulas), 4-P0891 (p.891 semiconductor chip example) and 4-P0892 (p.892 pipe volume graph example). Tests check that this calculator reproduces those values. For ejector flow and pipe conductance, use your product's catalogue.