CBR to Modulus of Subgrade Reaction Converter
Converts a subgrade CBR into the modulus of subgrade reaction k used in rigid (concrete) pavement and slab-on-ground design. It applies the AASHTO relation k = Mr / 19.4 via the resilient modulus and reports k in both pci and SI (MPa/m).
Enter Values
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How to use this calculator
- Enter the subgrade CBR as a percentage.
- Read the modulus of subgrade reaction k in pci and in MPa/m (= kPa/mm).
- Use the intermediate resilient modulus Mr (psi) to cross-check against other methods.
How it works
The modulus of subgrade reaction k relates the contact pressure under a rigid slab to its deflection and is the key subgrade input for concrete-pavement thickness design.
The calculator first estimates the resilient modulus, Mr = 1500 × CBR (psi), then applies the AASHTO conversion k = Mr / 19.4 to obtain k in pci. It converts to SI using 1 pci = 271.45 kN/m³ = 0.271447 MPa/m (equivalently 0.271447 kPa/mm), noting MPa/m and kPa/mm are numerically identical.
Worked example
CBR 5 subgrade. With CBR = 5 %: Mr = 1500 × 5 = 7500 psi; k = 7500 / 19.4 = 386.6 pci; and k = 386.6 × 0.271447 ≈ 104.9 MPa/m (104.9 kPa/mm).
Common mistakes
- Mixing up the SI scale — 1 pci is 0.271 MPa/m (≈ 271 kN/m³), not 271 MPa/m.
- Treating a CBR-derived k as a substitute for a plate load test; k is really a plate-load parameter and correlations are approximate.
- Using k in a flexible-pavement method — k is for rigid (concrete) design, whereas resilient modulus Mr drives flexible design.
Frequently asked questions
How do you convert CBR to modulus of subgrade reaction?
Estimate Mr = 1500 × CBR (psi), then k = Mr / 19.4 (AASHTO), giving k in pci. Convert to SI with 1 pci = 0.271447 MPa/m (= 271.45 kN/m³).
What is the SI unit of the modulus of subgrade reaction?
MPa/m (equivalently kPa/mm, or kN/m³). For CBR 5 the value is about 105 MPa/m.
Is CBR a reliable way to get k?
Only approximately. k is defined by a plate load test (AS 1289.6.9 / ASTM D1196); the CBR correlation is a preliminary estimate.
Why divide by 19.4?
19.4 is the AASHTO coefficient linking resilient modulus (psi) to the modulus of subgrade reaction (pci) for design, k = Mr / 19.4.
Related tools
- Subgrade Modulus Calculator
- CBR-Based Pavement Thickness Calculator
- Structural Number Calculator
- ESAL Traffic Loading Calculator
- Rigid Pavement Thickness Calculator
- AASHTO Flexible Pavement Thickness Calculator
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