Slab on Grade Thickness Calculator

Sizing a Slab-on-Grade for Interior Wheel Loads

A slab on grade is a concrete floor or pavement slab supported directly by prepared soil or a granular base rather than spanning between beams. Warehouses, factories, workshops, loading areas, equipment pads, agricultural buildings, and similar facilities commonly use this construction. Although the system appears simple, slab depth strongly affects service performance. A slab that is too thin for its wheel load and support condition can develop bottom-fiber tensile stress above the concrete's flexural strength, leading to cracking, reduced service life, maintenance disruption, and costly repairs.

This slab-on-grade thickness calculator estimates a required depth for an interior wheel load with Westergaard's plate-on-elastic-foundation theory. The model treats the concrete as an elastic plate and the soil or base as a spring-like support. That idealization is useful for preliminary slab sizing because it accounts for wheel load, tire contact area, concrete stiffness, slab thickness, and subgrade support. It is not a complete construction design, but it provides a practical starting point for comparing slab alternatives before more detailed checks.

The calculation is specifically for an interior load: the wheel is assumed to be far enough from free slab edges and corners that the slab extends effectively in every direction. Edge and corner loading can create higher stresses than this interior condition. Loads near joints, openings, pits, slab edges, or corners therefore need the applicable load-case equations or a more comprehensive slab-design review; relying on this interior-load result alone may be unconservative.

How to Use the Slab-on-Grade Thickness Calculator

For this interior wheel-load slab check, enter wheel load, contact radius, subgrade modulus, concrete modulus, Poisson's ratio, and flexural strength in the six fields below, then press Compute Thickness. The calculator begins with a 100 mm trial slab and raises the trial depth by 5 mm at a time. At each depth it recalculates bending stress until that stress is no greater than the entered flexural strength. The result reports the first passing thickness and its induced interior stress, letting you see whether the practical minimum governs or the flexural limit controls.

Each slab-design input has a distinct role. Wheel Load P (kN) is one wheel load or one equivalent concentrated load delivered to the slab; do not enter total vehicle weight unless a single wheel carries it. Contact Radius a (m) is the radius of the circular load-transfer area. A larger contact area spreads load and generally lowers calculated stress. Subgrade Modulus k (MPa/m) represents foundation stiffness. Higher support values generally reduce slab stress and can permit a thinner slab.

Concrete Modulus E (MPa) is the concrete elastic modulus used in the plate-stiffness calculation. Poisson's Ratio ν represents lateral strain response and is often taken near 0.15 for a preliminary concrete slab estimate. Concrete Flexural Strength R (MPa) is the modulus of rupture or bending-stress limit against which the computed interior stress is checked. Use a project-specified, tested, or otherwise appropriate value for the concrete mix and curing condition.

Keep the slab calculator's units consistent: enter wheel load in kilonewtons, geometry in meters, and material/support values in MPa or MPa per meter as labeled. Convert outside values before entry. Frequent errors include mixing millimeters and meters, using axle or vehicle weight instead of one wheel load, and entering contact diameter when the form requests radius. Such conversion mistakes can change the resulting slab depth substantially.

Westergaard Formula and Slab-Thickness Calculation Basis

The Westergaard interior-wheel-load calculation first evaluates the slab's radius of relative stiffness, a measure of how the concrete plate distributes load across its supporting foundation. A larger relative-stiffness radius indicates that the slab is stiffer relative to the subgrade and can spread a wheel load over a wider area. The calculator uses:

Using that relative stiffness, the calculator estimates bottom-fiber interior tensile stress beneath the wheel as:

The slab-depth search seeks a thickness for which calculated interior stress does not exceed the selected concrete flexural strength:

In these slab equations, $a$ is contact radius, $h$ is slab thickness, $E$ is concrete modulus, $k$ is subgrade modulus, $\nu$ is Poisson's ratio, and $R$ is the concrete flexural-strength limit. Since thickness affects both relative stiffness and the stress denominator, this implementation does not use a one-step algebraic rearrangement. It starts at 0.1 m, computes relative stiffness and stress, and adds 0.005 m per iteration until stress is at or below the entered flexural strength or the loop reaches its limit.

This stepped slab-thickness search is easy to inspect and matches the way preliminary trial depths are often compared. Its result is a rational estimate at the script's 5 mm increment, not a continuously optimized final design. Final slab-on-grade design may also require checks for joints, fatigue, reinforcement, curling, drainage, and construction tolerance.

A 40 kN Forklift Wheel Slab-Thickness Example

With the form's default slab inputs—a 40 kN wheel, 0.15 m contact radius, 50 MPa/m subgrade modulus, 30,000 MPa concrete modulus, 0.15 Poisson's ratio, and 4.5 MPa flexural strength—the first 0.100 m trial slab passes. The calculated interior tensile stress is about 1.70 MPa, below the 4.5 MPa limit. Under this simplified interior-load check, the 100 mm practical minimum governs rather than flexure. That result can indicate that constructability, joint layout, or wear requirements may set the selected floor thickness instead.

To see the slab-depth iteration respond to a more demanding interior load, change the wheel load to 200 kN and the subgrade modulus to 30 MPa/m while leaving the other inputs unchanged. The stress at 100 mm is too high, so the script increases depth in 5 mm steps until it reaches approximately 0.135 m. At that depth the induced stress is about 4.38 MPa, just below the 4.5 MPa limit. This comparison shows how a larger concentrated wheel load and weaker support can make flexure, rather than the practical minimum, control the slab thickness.

The example also illustrates why tire contact radius needs careful input. Wheels with identical load can produce different slab demands when their footprints differ. A larger contact radius lowers local stress concentration in this model and can reduce the depth required by the interior-load calculation. Tire pressure, wheel type, support quality, load repetition, and environmental exposure remain relevant to the final engineering decision.

Understanding Slab Support and Concrete Inputs

For slab-on-grade sizing, users often know the wheel load but have less certainty about the supporting and material properties. Subgrade modulus is especially consequential because it represents support from soil and base beneath the slab. Weak, wet, or poorly compacted support permits more deflection and typically raises slab stress. A well-prepared granular base over competent soil improves support and can reduce the depth required for the same wheel load. Because support can vary across a site, an optimistic value may not represent the governing condition.

Concrete modulus and concrete flexural strength describe different slab properties. Elastic modulus is a stiffness measure: it affects how the slab spreads load while behaving elastically. Flexural strength is the bending stress at which cracking is expected. A concrete mix can have one property without an equivalent increase in the other, so both are needed in this Westergaard-based calculation—one influences load distribution and the other defines the stress limit.

Poisson's ratio usually has less influence on the computed slab depth than wheel load, contact radius, or subgrade modulus, but it remains part of elastic plate behavior. A value near 0.15 is commonly used for an early normal-concrete estimate when project-specific data are unavailable. Contact radius also deserves review: for a noncircular tire footprint, an equivalent circular contact area may be used so this simplified Westergaard equation can be applied.

Slab-on-Grade Assumptions and Input Guidance

This interior wheel-load slab method assumes a homogeneous, isotropic concrete plate on uniformly supported elastic foundation material, with a static load spread over a circular contact area. Those assumptions make early slab sizing manageable but simplify field conditions. Actual floors can have variable support, moisture changes, curling, joint movement, repeated traffic, and construction tolerances. Use the calculator as an early design aid, teaching tool, or comparison method rather than as the sole basis for construction documents.

For preliminary slab studies, subgrade modulus may be estimated from plate-load testing or correlations with soil and base conditions. The following values are only illustrative and do not replace site-specific investigation:

Actual slab support depends on moisture, compaction, base thickness, frost susceptibility, drainage, and long-term settlement. Heavy industrial traffic, sensitive equipment, substantial rack loads, or stringent flatness requirements warrant geotechnical input and a more detailed slab-design procedure. The same applies where the floor must perform for many years with little tolerance for cracking or differential settlement.

Reading Slab Thickness and Interior Stress Together

The reported slab thickness is the first trial depth that passes the interior flexural-stress check. Since the script searches in 0.005 m increments, the result follows that 5 mm step size. Designers commonly select a practical construction thickness after this calculation, then reconsider joints, reinforcement, tolerances, durability, and whether the rounded construction thickness remains appropriate.

The induced interior stress provides important context for the slab depth. Stress only slightly below flexural strength indicates little reserve within this simplified model. Stress comfortably below the limit indicates more modeled margin, though it does not prove that the slab is overdesigned because important field conditions lie outside the equation. Reading stress with thickness helps identify whether modest changes in wheel load or support could affect the result.

This slab calculator is also useful for comparing related conditions. Hold wheel load fixed while changing subgrade modulus to explore the potential value of base improvement, or compare contact radii to see the modeled effect of tire pressure and wheel type. Such comparisons help identify whether load, tire footprint, or support stiffness is most influential for a proposed slab-on-grade condition.

Interior Wheel-Load Limitations and Engineering Judgment

This calculator evaluates only the Westergaard interior load condition for a slab on grade. It does not directly check edge or corner loading, doweled joints, distributed rack-post loads, line loads, multiple-wheel interaction, or combined loading patterns. These conditions can create higher stresses and may require more thickness, reinforcement, joint detailing, or another design method. Saw-cut joints, construction joints, and free edges near a loaded area need separate consideration.

The calculation also excludes fatigue from repeated traffic, moving-load impact, temperature and moisture curling, shrinkage restraint, cracking from settlement, and post-cracking contribution from reinforcement or fibers. Reinforcement can improve crack control and post-cracking behavior, but it does not automatically replace sufficient concrete depth. Similarly, stronger concrete does not correct weak support, poor joint performance, or inadequate drainage.

The script's fixed iteration range is another practical constraint. It increases thickness by set increments and stops after a set number of trials, making the tool quick and transparent but approximate. For concept comparisons that approach is useful. Final engineering decisions involving safety, durability, or operational reliability should be reviewed by a qualified engineer against applicable project standards, local requirements, and observed field conditions.

Use this slab-on-grade thickness calculator to understand wheel-load trends and obtain a first-pass interior-load depth. Confirm a final slab with the broader considerations real floors and pavements require, including support uniformity, joint spacing, load transfer, construction quality, drainage, curling control, expected traffic, and the consequences of cracking or settlement.

Slab-on-Grade Formula Reference Summary

The interior-wheel-load relationships used by this calculator are summarized below in MathML for accessible formula reference. They define the entered slab variables, the relative-stiffness trend, and the principal stress trends used in the iterative depth search.