Modulus of Elasticity of Concrete
Concrete stiffness is earned, not specified: it follows the compressive strength, and the codes give a square root formula rather than a single number.
| fc = 20 MPa | about 21.0 GPa |
| fc = 25 MPa | about 23.5 GPa |
| fc = 30 MPa | about 25.7 GPa |
| fc = 35 MPa | about 27.8 GPa |
| fc = 40 MPa | about 29.7 GPa |
| fc = 50 MPa | about 33.2 GPa |
| CSA A23.3, normal density | Ec = 4500 √fc, slightly softer |
| ACI in psi units | Ec = 57000 √fc psi |
Notes for design and site
The CSA full formula adds what the shortcut hides: Ec = (3300 √fc + 6900) times (density over 2300) to the power 1.5. Density is the quiet variable, and it is why lightweight concrete gives up 25 to 40 percent of its stiffness even at the same strength. At 30 MPa and normal density the full formula lands on 25.0 GPa, close enough to the shortcuts that either serves for sizing.
Treat every value here as more approximate than the steel page next door. Concrete cracks, and cracked sections are far softer than gross ones; it also creeps, so sustained load deflections run two to three times the elastic figure. That is why deflection checks in concrete design revolve around effective moment of inertia and long term multipliers rather than the bare Ec.
Related Calculators and Reference
- RC Beam Design Calculator: where Ec meets the cracked section.
- Unit Weight of Concrete: the density term in the CSA formula.
- Modulus of Elasticity of Steel: the constant neighbour, eight times stiffer.
- Elastic Moduli Interconversion Calculator: from Ec to shear and bulk modulus.
- American Concrete Institute: the code body behind the 4700 root fc formula.