Calculate short, metric or long ton-force from pressure and area, or estimate cylinder push and pull force from pressure, bore and optional rod diameter.
| PSI to Short Tons | Short Tons to PSI |
|---|---|
| 250 psi = 0.125 short tons | 0.1 short tons = 200 psi |
| 500 psi = 0.25 short tons | 0.25 short tons = 500 psi |
| 750 psi = 0.375 short tons | 0.3 short tons = 600 psi |
| 1,000 psi = 0.5 short tons | 0.5 short tons = 1,000 psi |
| 1,200 psi = 0.6 short tons | 0.75 short tons = 1,500 psi |
| 1,500 psi = 0.75 short tons | 1 short ton = 2,000 psi |
| 1,750 psi = 0.875 short tons | 1.5 short tons = 3,000 psi |
| 2,000 psi = 1 short ton | 2 short tons = 4,000 psi |
| 2,250 psi = 1.125 short tons | 2.5 short tons = 5,000 psi |
| 2,500 psi = 1.25 short tons | 3 short tons = 6,000 psi |
| 2,750 psi = 1.375 short tons | 4 short tons = 8,000 psi |
| 3,000 psi = 1.5 short tons | 5 short tons = 10,000 psi |
| 3,200 psi = 1.6 short tons | 7.5 short tons = 15,000 psi |
| 3,500 psi = 1.75 short tons | 10 short tons = 20,000 psi |
| 4,000 psi = 2 short tons | 12 short tons = 24,000 psi |
| 4,500 psi = 2.25 short tons | 15 short tons = 30,000 psi |
| 5,000 psi = 2.5 short tons | 20 short tons = 40,000 psi |
| 6,000 psi = 3 short tons | 25 short tons = 50,000 psi |
| 7,000 psi = 3.5 short tons | 30 short tons = 60,000 psi |
| 10,000 psi = 5 short tons | 50 short tons = 100,000 psi |
| Formula (A = 1 in2): short tons = psi / 2000; psi = short tons x 2000. | |
| Bore (in) to Short Tons | Short Tons to Required Bore (in) |
|---|---|
| 2 in bore = 4.712 short tons | 5 short tons = 2.060 in bore |
| 2.5 in bore = 7.363 short tons | 10 short tons = 2.913 in bore |
| 3 in bore = 10.603 short tons | 20 short tons = 4.120 in bore |
| 4 in bore = 18.850 short tons | 30 short tons = 5.046 in bore |
| 5 in bore = 29.452 short tons | 50 short tons = 6.515 in bore |
| Formula: area = πd²/4; short ton-force = (psi x area) / 2000. Ideal force; opposite-side gauge pressure and friction are neglected. | |
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psi to Tons Formula
The core relationship linking pressure to force is:
Variables:
- F is short ton-force (1 short ton-force = 2,000 lbf), not mass
- P is the applied gauge pressure in pounds-force per square inch (psi), with the opposite side assumed at zero gauge pressure
- A is the effective area the pressure acts on, in square inches
The formula rearranges to solve for any unknown. To find pressure: P = (F x 2000) / A. To find area: A = (F x 2000) / P. For metric tons, replace 2,000 with 2,204.62 (pounds per metric ton). For long tons, use 2,240.
Short Ton vs. Metric Ton vs. Long Ton
The mass units short ton, metric tonne and long ton define corresponding ton-force units under standard gravity. The calculator reports force, not mass; mixing these force units can cause significant engineering errors. A short ton (US ton) equals 2,000 pounds (907.185 kg) and is the standard in American industry. A metric ton (tonne) equals 1,000 kg or 2,204.62 pounds, and is the international standard used in most countries outside the US. A long ton (imperial ton) equals 2,240 pounds (1,016.047 kg) and is still used in British shipping and some legacy specifications. The difference between a short ton and a metric ton is roughly 10%, which matters significantly when sizing hydraulic equipment or specifying press tonnage for international orders.
Why psi Cannot Be Directly Converted to Tons
psi is pressure, while ton-force is force. Pressure alone cannot determine force without an effective area. At 3,000 psi, a 1-inch bore produces about 1.18 US short ton-force and a 4-inch bore about 18.85 US short ton-force, assuming full piston area, zero opposite-side gauge pressure and no friction. Force scales with the square of bore diameter.
Hydraulic Cylinder Tonnage
In hydraulic systems, the effective piston area determines tonnage output. For a single-acting cylinder on the push stroke, area = pi x d2 / 4, where d is the bore diameter. On the retract (pull) stroke, the rod cross-section is subtracted: effective area = pi x (d_bore2 – d_rod2) / 4. For a positive rod diameter, identical applied pressure and zero opposite-side gauge pressure, ideal pull force is below push force. These calculations do not establish rated capacity. A 4-inch bore cylinder with a 2-inch rod at 3,000 psi pushes 18.85 short tons but pulls only 14.14 short tons, a 25% reduction.
Bore size has a squared relationship to force output. Doubling the bore diameter from 2 inches to 4 inches increases tonnage by 4x, not 2x. Tripling the bore to 6 inches increases tonnage by 9x. This is why small increases in cylinder bore diameter yield large gains in press capacity.
Hydraulic Press Tonnage by Application
Press force requirements vary with the process, material, geometry, tooling and duty. No universal tonnage range establishes safe equipment selection. SINOMACH describes an 80,000-ton forging press; that nominal equipment description is not a direct pressure conversion.
Real-World Pressure Benchmarks in psi
Pressure in fluid systems and stress in materials both use psi, but a material strength must not be treated as an allowable hydraulic pressure. For example, SAE J429 Grade 8 fasteners in the listed ¼–1½-inch range have minimum yield strength of 130,000 psi and minimum tensile strength of 150,000 psi. These specifications do not establish a safe assembly load or hydraulic-system pressure. Use the actual component and equipment ratings.
Factors That Reduce Actual Tonnage Output
The formula gives ideal static force or force adjusted by the entered delivered-force factor. Actual cylinder force depends on both chamber pressures, return backpressure, seal friction and operating conditions. For extension, the pressure force is cap-side pressure × full piston area minus rod-side pressure × annular area; friction also reduces delivered force. Use manufacturer data or measured performance. There is no universal correction factor.
Sizing a Hydraulic Cylinder from Target Tonnage
When the required force is known and the goal is to select a cylinder, rearrange the formula to solve for bore diameter: d = sqrt(F x 2000 x 4 / (pi x P)). For example, if a press brake application needs 25 short tons at a system pressure of 3,000 psi, the required bore is sqrt(25 x 2000 x 4 / (3.14159 x 3000)) = 4.607 inches. This is a theoretical area requirement, not a safety margin or equipment selection. Final bore, rod, mounting and pressure ratings must account for backpressure, friction, buckling, duty and manufacturer limits. Standard hydraulic cylinder bore sizes in NFPA and ISO catalogs include 1.5, 2, 2.5, 3, 3.25, 3.5, 4, 4.5, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, and 24 inches.
