Calculate compressive strength, force, or loaded area from two known values with unit conversions for N, kN, lbf, m², cm², ft², in², MPa, and psi.
Compressive Strength Formula
The basic compressive strength formula is force divided by loaded area. If the entered force is the failure load, the result is compressive strength. If the entered force is a working load or any non-failure load, the result is compressive stress at that load.
CS = F / A
- CS = compressive strength or compressive stress
- F = maximum compressive force, usually the failure load
- A = loaded cross-sectional area
To solve for compressive force:
F = CS * A
To solve for loaded area:
A = F / CS
The calculator lets you enter any two values and solves for the missing one:
- Compressive strength or stress: calculated from force divided by area.
- Maximum compressive force: calculated from strength multiplied by area.
- Loaded area: calculated from force divided by strength.
Calculations are converted internally to base SI units: newtons for force, square meters for area, and N/m² for strength or stress. The final answer is then converted back to the unit you selected.
Common Compressive Strength and Stress Units
| Unit | Equivalent | Common use |
|---|---|---|
| N/m² | 1 Pa | Base SI stress unit |
| kN/m² | 1,000 N/m² | Soils, bearing pressure, light structural loads |
| MPa | 1,000,000 N/m² | Concrete, metals, engineered materials |
| psi | 6,894.76 N/m² | US customary material testing and pressure values |
Typical Compressive Strength Ranges
| Material | Typical compressive strength | Notes |
|---|---|---|
| Normal concrete | 20 to 40 MPa | Depends on mix, curing, and test age |
| High-strength concrete | 40 to 100 MPa | Used where higher load capacity is needed |
| Common clay brick | 10 to 30 MPa | Varies widely by brick type and manufacturing |
| Softwood parallel to grain | 20 to 50 MPa | Moisture and grain direction strongly affect strength |
Example Calculations
Example 1: Find compressive strength
A specimen fails under a compressive load of 200 kN. The loaded area is 0.01 m².
CS = F / A
CS = 200000 / 0.01 = 20000000 N/m^2
The compressive strength is 20,000,000 N/m², or 20 MPa.
Example 2: Find failure load
A material has a compressive strength of 30 MPa and a loaded area of 50 cm².
Convert the values first:
- 30 MPa = 30,000,000 N/m²
- 50 cm² = 0.005 m²
F = CS * A
F = 30000000 * 0.005 = 150000 N
The failure load is 150,000 N, or 150 kN.
FAQ
What is the difference between compressive stress and compressive strength?
Compressive stress is the force per unit area at any given load. Compressive strength is the maximum compressive stress a material can withstand before failure. The formula is the same, but the meaning depends on the force you enter. If you enter the failure load, the result is strength. If you enter a smaller applied load, the result is stress.
Which area should be used in the compressive strength formula?
Use the loaded cross-sectional area that directly carries the compressive force. For a cylinder, this is the circular face area. For a cube or rectangular specimen, this is the face area under compression. Do not use total surface area unless the entire surface is actually loaded in compression.
Why are MPa and psi common for compressive strength?
Compressive strength values are often large when expressed in N/m², so MPa gives a more practical number in SI units. For example, 20,000,000 N/m² is 20 MPa. In US customary units, psi is commonly used for concrete, masonry, and material test results.
