Enter the pressure in psi and the area over which it is applied in square inches into the calculator to determine the force in tons. This calculator converts between pressure (psi), area (sq in), and force (tons), and includes a dedicated hydraulic cylinder tonnage mode for bore-based calculations.
| 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 = pid2/4; short tons = (psi x area) / 2000. | |
- All Unit Converters
- Thermodynamics and Fluid Unit Converts
- PSI To Volume Calculator
- PSI to Force Calculator
- Grams To Psi Calculator
Psi to Tons Formula
The core relationship linking pressure to force is:
F (short tons) = P (psi) x A (in2) / 2000
Variables:
- F is the force in short tons (1 short ton = 2,000 lb)
- P is the gauge pressure in pounds per square inch (psi)
- 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
Three different “ton” definitions exist, and mixing them up 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 a unit of pressure (force per unit area), while a ton is a unit of force (or mass). These are fundamentally different physical quantities. Pressure alone does not determine force without knowing the area over which it acts. A hydraulic system at 3,000 psi produces 2.36 short tons through a 1-inch bore cylinder but 37.7 short tons through a 4-inch bore, because the piston area scales with the square of the diameter. This is why the calculator above requires both pressure and area inputs.
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. This means pulling capacity is always less than pushing 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
Different industrial processes require vastly different tonnage ranges. Benchtop presses used for bearing and bushing installation typically operate in the 1 to 30 ton range at 3,000 to 5,000 psi. General metal fabrication and auto shop H-frame presses cover the 50 to 150 ton range. Stamping presses for automotive body panels run from 200 to 1,000 tons. Deep-draw forming of complex shapes requires 500 to 2,000 tons. Forging presses for structural steel and aerospace components start at 1,000 tons and can exceed 50,000 tons for large open-die forging of turbine shafts and landing gear. The world’s largest hydraulic press operates at approximately 200,000 tons (China’s 80,000 metric ton die forging press in Deyang), used for producing single-piece titanium and high-strength alloy forgings for aircraft.
Real-World Pressure Benchmarks in Psi
Understanding where common pressures fall helps contextualize psi-to-ton calculations. Standard residential water pressure is about 40 to 80 psi. A car tire runs at 30 to 35 psi. Residential concrete has a compressive strength of 2,500 to 5,000 psi, while high-performance concrete used in bridges and high-rises reaches 10,000 to 15,000 psi. Standard hydraulic systems operate at 3,000 to 5,000 psi, with high-pressure systems reaching 10,000 psi. Ultra-high-pressure waterjet cutting systems operate at 60,000 to 90,000 psi. Structural steel (A36) has a yield strength of about 36,000 psi (equivalent to 18 short tons per square inch), and high-strength bolt steel (Grade 8) reaches 150,000 psi yield. Prestressing steel tendons used in bridges operate at tensile strengths of 250,000 to 270,000 psi.
Factors That Reduce Actual Tonnage Output
Calculated tonnage from the formula above represents theoretical maximum output. In practice, several factors reduce actual delivered force. Cylinder seal friction consumes 3% to 10% of theoretical force depending on seal type and condition. Pressure drops through valves, fittings, and hose runs can reduce effective cylinder pressure by 5% to 15% below the pump’s rated output. Entrained air in the hydraulic fluid reduces system stiffness and can cause spongy, inconsistent force delivery. Gauge calibration drift means the pressure reading may not reflect actual line pressure. Temperature also plays a role: hydraulic oil viscosity increases at low temperatures, raising system pressure losses, while high temperatures reduce oil viscosity and can cause internal pump and valve leakage. A common industry rule of thumb applies a 0.85 to 0.90 efficiency factor to theoretical tonnage calculations to account for these real-world losses.
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. In practice, you would select the next standard bore size up (typically 5 inches) to provide a safety margin. 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.
