How do you calculate hydraulic cylinder force from pressure and bore?

Cylinder force (F in N) equals hydraulic pressure (P in Pascals) multiplied by the piston cross-sectional area (A = π × r² in m²): F = P × A. For a 100mm (0.1m) bore cylinder operating at 200 bar (20,000,000 Pa), force = 20,000,000 × (π × 0.05²) = 157,080 N ≈ 157.1 kN (35,314 lbf or 16.0 metric tons).

What is the formula to convert PSI to cylinder clamp force?

Force in pounds (lbf) = Pressure (PSI) × Area (square inches). A 4-inch bore cylinder has an area of π × 2² ≈ 12.57 in². At 3,000 PSI hydraulic pressure, force = 3,000 × 12.57 = 37,710 lbf (18.85 US tons).

Square Centimeter to Square Inch (cm² to in²) Calculator & Formula

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Live Conversion • ISO 80000-3:2019 Certified

1 Square Centimeter = 0.15500031 Square Inch

1 cm² = 0.155 in² • 1 in² = 6.4516 cm²

Decimals:

Certified Authority Value

0.15500031

in²

From / Input

cm²

Swap to Square Inch to Square Centimeter

To / Result

in²

Quick Values:

1 cm² 5 cm² 10 cm² 25 cm² 50 cm² 100 cm² 250 cm² 500 cm² 1,000 cm²

Conversion Formula

To convert Square Centimeter to Square Inch, multiply by 0.15500031

cm² × 0.15500031 = in²

Calculation: 1 cm² × 0.15500031 = 0.15500031 in²

Common Square Centimeter to Square Inch Calculations

Quick-lookup reference table showing calculated equivalents for standard increments between Square Centimeter (cm²) and Square Inch (in²).

Tap any row to calculate

Square Centimeter to Square Inch: Primary Direct Table (15 Steps)

Rule: 1 Square Centimeter is equal to 0.155 in² (Square Inch)

Square Centimeter to Square Inch Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 cm² is equal to 0.000155 in² (Square Inch)	1.55 × 10⁻⁴
0.01 cm² is equal to 0.00155 in² (Square Inch)	1.55 × 10⁻³
0.1 cm² is equal to 0.0155 in² (Square Inch)	1.55 × 10⁻²
0.5 cm² is equal to 0.0775002 in² (Square Inch)	7.75 × 10⁻²
1 cm² is equal to 0.155 in² (Square Inch)	1.55 × 10⁻¹
2 cm² is equal to 0.310001 in² (Square Inch)	3.1 × 10⁻¹
5 cm² is equal to 0.775002 in² (Square Inch)	7.75 × 10⁻¹
10 cm² is equal to 1.550003 in² (Square Inch)	1.55 × 10⁰
20 cm² is equal to 3.100006 in² (Square Inch)	3.1 × 10⁰
25 cm² is equal to 3.875008 in² (Square Inch)	3.875 × 10⁰
50 cm² is equal to 7.750016 in² (Square Inch)	7.75 × 10⁰
100 cm² is equal to 15.500031 in² (Square Inch)	1.55 × 10¹
250 cm² is equal to 38.750078 in² (Square Inch)	3.875 × 10¹
500 cm² is equal to 77.500155 in² (Square Inch)	7.75 × 10¹
1000 cm² is equal to 155.00031 in² (Square Inch)	1.55 × 10²

Square Inch to Square Centimeter: Reciprocal Summary

Rule: 1 Square Inch is equal to 6.4516 cm² (Square Centimeter)

Square Inch to Square Centimeter Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 in² is equal to 6.4516 cm² (Square Centimeter)	6.452 × 10⁰
5 in² is equal to 32.258 cm² (Square Centimeter)	3.226 × 10¹
10 in² is equal to 64.516 cm² (Square Centimeter)	6.452 × 10¹
50 in² is equal to 322.58 cm² (Square Centimeter)	3.226 × 10²
100 in² is equal to 645.16 cm² (Square Centimeter)	6.452 × 10²

View Complete 15-Row Square Inch to Square Centimeter Table

Real-World Context & Everyday Benchmarks

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To help contextualize these units in everyday life, science, and engineering, here are verified real-world reference points for Square Centimeter (cm²) and Square Inch (in²):

Square Centimeter References:

Standard international postage stamp paper surface area 5 cm²
Standard plastic banking credit card front surface face area 46 cm²
Standard smartphone touchscreen front glass display area 90 cm²

Square Inch References:

Standard yellow square Post-it sticky reminder memo note area (3x3 in) 9 sq in
United States official passport biometric identification photograph area 4 sq in

Tap any benchmark above to automatically calculate its exact equivalent in Square Inch.

ISQ Dimension: [L²] Coherent SI Unit: square meter (m²) Classical Mechanics & Dimensional Metrology

How to Convert Square Centimeter to Square Inch

Converting Square Centimeter (cm²) to Square Inch (in²) is a core calculation in Surface Area, which measures the two-dimensional extent of a surface, planar boundary, or land parcel. This calculation navigates the boundary between the International Metric System (SI) and British Imperial / US Customary engineering standards. In contemporary metrology, Imperial units are defined in terms of exact SI standards via international agreements—notably NIST SP 811 and the 1959 International Yard and Pound Agreement. Exactly 1 Square Centimeter equals 0.155 Square Inch, while 1 in² equals 6.4516 cm².

Direct Factor1 cm² = 0.155 in²

Inverse Ratio1 in² = 6.4516 cm²

Conversion ScaleMetric SI to British Imperial / US Customary Bridge

First-Principles SI Derivation ProofNIST SP 811 / ISO 80000 Compliance

Mathematical Conversion Derivation via Coherent SI Base Unit

Under the International System of Quantities (ISQ), dimensional conversion between non-SI units is rigorously resolved by bridging through the coherent SI base unit (square meter (m²)) without arbitrary rounding:

V_{\text{target}} = V_{\text{source}} \times \left( \frac{k_{\text{source} \to \text{SI}}}{k_{\text{target} \to \text{SI}}} \right)

Universal Dimensional Conversion Law (ISO 80000 / NIST SP 811)

1. Source SI Bridge (k_source):1 cm² = 0.0001 square meter (m²)

2. Target SI Bridge (k_target):1 in² = 0.00064516 square meter (m²)

Step-by-step substitution for Square Centimeter → Square Inch:V(in²) = V(cm²) × ( 0.0001 / 0.00064516 ) = V(cm²) × 0.155

Mathematical FormulaValue in Square Inch = Value in Square Centimeter × 0.15500031Direct computational formula applied for standard conversion.

Worked Example

To convert 12 Square Centimeter (cm²) to Square Inch (in²): multiply 12 by 0.155 to get 1.860004 in². At an industrial engineering scale, 240 cm² converts to 37.200074 in².

Inverse check: 1 in² = 6.4516 cm².

Understanding Square Centimeter and Square Inch

Domain Metrology & Engineering Applications

Governing Law & Equation

Euclidean 2D Surface Integration (A = ∬ dx dy)

Measurement Instrumentation

Rigorously quantified in laboratory and field settings using planimeters, GIS spatial mapping tools, laser surface scanners, and geodetic boundary transits.

Primary Industry Sectors

Applied across real estate cadastral surveying, agricultural land management, architectural design, and civil civil engineering under international metrology standard ISO 80000-3:2019, NIST SP 811.

Physical Orders of Magnitude & Laboratory Reference Benchmarks

Physical Phenomenon / Engineering Reference	Reference Value	Converted to Square Inch
Standard international postage stamp paper surface area	`5 cm²`	`0.775002 in²`
Standard plastic banking credit card front surface face area	`46 cm²`	`7.130014 in²`
Standard smartphone touchscreen front glass display area	`90 cm²`	`13.950028 in²`

Institutional Metrology & Standard Authority:

Formulas, conversion coefficients, and base definitions on this page strictly adhere to the ISO 80000-3:2019, NIST SP 811 and the BIPM SI Brochure (9th Edition). Governed by Euclidean 2D Surface Integration (A = ∬ dx dy) under ISO 80000 dimensional vector [L²].

Multi-Variable Engineering Bridge Fluid Power & Contact Mechanics

Hydraulic Cylinder & Contact Force Bridge (kN • lbf • Metric Tons • Bar • PSI • Pascals)

Calculate total thrust, clamp load, or bolt pretension from hydrostatic pressure [M L⁻¹ T⁻²] acting over cross-sectional geometry [L²] via Pascal's hydraulic principle F = P × A.

Input System Pressure (P): cm²

Select Cylinder Bore / Contact Geometry: 0.0079 m²

Coupling: F = P × A

Forward Reverse

Live Calculated Bridge Equivalent:

1 cm² at 100mm (4-inch) Standard Industrial Hydraulic Bore = 7.854 × 10⁻¹⁰ kN

Equals 1.7656 × 10⁻⁷ lbf • 8.0088 × 10⁻¹¹ t-force • 7.854 × 10⁻⁷ N

Civil & Press Metric

7.854 × 10⁻¹⁰

Kilonewtons

US Hydraulic Standard

1.7656 × 10⁻⁷

lbf

Pounds-Force

Press Capacity

8.0088 × 10⁻¹¹

t-force

Metric Tons Force

SI Standard

7.854 × 10⁻⁷

Newtons

US Press Rating

8.8282 × 10⁻¹¹

ton-force (US)

Short Tons Force

Workshop Standard

8.0089 × 10⁻⁸

kgf

Kilograms-Force

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (Pa):
P = 1 cm² × 0.0001 = 0.0001 Pa
2. Apply Engineering Parameter (A):
Selected condition: 100mm (4-inch) Standard Industrial Hydraulic Bore at A = 0.007854 m²
3. Execute Governing Physical Law in SI Units:
F = P × A = (0.0001) × (0.007854) = 7.854 × 10⁻⁷ N
4. Convert to Standard Engineering Units:
• kN: 7.854 × 10⁻⁷ × 0.001 = 7.854 × 10⁻¹⁰ kN (Kilonewtons) • lbf: 7.854 × 10⁻⁷ × 0.2248 = 1.7656 × 10⁻⁷ lbf (Pounds-Force) • t-force: 7.854 × 10⁻⁷ × 0.000102 = 8.0088 × 10⁻¹¹ t-force (Metric Tons Force) • N: 7.854 × 10⁻⁷ × 1 = 7.854 × 10⁻⁷ N (Newtons) • ton-force (US): 7.854 × 10⁻⁷ × 0.0001124 = 8.8282 × 10⁻¹¹ ton-force (US) (Short Tons Force) • kgf: 7.854 × 10⁻⁷ × 0.102 = 8.0089 × 10⁻⁸ kgf (Kilograms-Force)

Explore Full Area Converter →

Engineering Substance / Operating Standard	Parameter Value (m²)	Reference State / Condition	Typical Industrial & Engineering Application
25mm (1-inch) Micro Pneumatic Bore	`0.0004909`	Area = π × (0.0125m)²	Automation grippers & electronic assembly tooling
50mm (2-inch) Medium Pneumatic Ram	`0.001964`	Area = π × (0.025m)²	Industrial packaging presses & clamping fixtures
100mm (4-inch) Standard Industrial Hydraulic Bore	`0.007854`	Area = π × (0.05m)²	Excavator booms, log splitters & machine shop presses
150mm (6-inch) Heavy Mobile Hydraulic Ram	`0.01767`	Area = π × (0.075m)²	Mining shovels, dump truck lifts & forge actuators
200mm (8-inch) Massive Press Cylinder	`0.03142`	Area = π × (0.10m)²	Automotive body stamping presses & scrap balers
Vehicle Road Contact Patch (4 Car Tires)	`0.06`	4 × 150 cm² tire patches	Total passenger tire road contact footprint
Standard M12 High-Strength Bolt Tensile Area	`8.43 × 10⁻⁵`	ISO 898-1 stress area 84.3 mm²	Flange fastener clamping stress analysis
Standard M20 Structural Bolt Tensile Area	`0.000245`	Stress area 245 mm²	Heavy structural steel framing & anchor rods
1.0 Square Meter Reference Plate Area	`1`	1.0 m × 1.0 m area	Architectural wind load & hydrostatic flood gate

Frequently Asked Questions

There are exactly 0.15500031 square inches (in²) in 1 square centimeter (cm²). To calculate larger amounts manually, simply multiply your total number of square centimeters by the conversion multiplier of 0.15500031.

The mathematical formula to convert square centimeters to square inches is: [value] * 0.15500031 = square inches. Rather than doing the math manually, you can use our high-precision online calculator to process this exact equation instantly without rounding errors.

To perform the reverse calculation from square inches back to square centimeters, you must divide your starting value by 0.15500031. Our bidirectional tool automatically computes this inverse equation the moment you type into the square inch input field.

1 Square Inch is larger than 1 Square Centimeter. Specifically, 1 Square Centimeter equals 0.15500031 square inches, meaning 1 Square Inch is 6.4516 times larger than 1 Square Centimeter (a difference of 0.81 orders of magnitude). Expressing measurements in square centimeters requires a larger numerical value to represent the equivalent physical magnitude.

A typical standard international postage stamp paper surface area measures 5 cm², which corresponds to 0.775 in² (Square Inch).

The standard metric-to-imperial area constant is exactly 1 cm² = 0.155 in².

The translation equation is V(in²) = V(cm²) × 0.155.

The exact inverse formula for machining precision is V(cm²) = V(in²) × 6.4516.

This factor (0.155) is universally applied in mechanical design and fluid dynamics when converting internal pipe pressure from kg/cm² to lbs/in² (PSI).

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