Concrete Shrinkage Calculator

Inputs

Example data table

These examples show common input ranges; verify project assumptions and standards.

Formula used

This calculator follows the shrinkage form presented in ACI 209.2R-08 Appendix A (B3-based):

• εsh(t,tc) = εsh∞ · kh · S(t−tc)
• εsh∞ = α1 · α2 · [0.019·w^2.1·fcm28^−0.28 + 270] · 10^−6 (mix-based), or nominal 780 µε
• kh = 1 − h^3 for h ≤ 0.98; linear interpolation for 0.98<h<1; kh = −0.2 at h = 1.0
• τsh = 0.085 · tc^−0.08 · fcm28^−0.25 · [2·ks·(V/S)]^2
• S(t−tc) = tanh( √((t−tc)/τsh) )
• ΔL = εsh · L

Units: RH in %, h in decimals, w in kg/m³, fcm28 in MPa, V/S in mm, time in days.

How to use this calculator

1. Set t as the age when shrinkage is needed.
2. Set tc as the end of moist curing (drying start).
3. Enter average RH and a reasonable V/S for the member.
4. Pick cement and curing method to apply α-factors.
5. Choose mix-based for εsh∞, or use nominal if unknown.
6. Enter member length L to estimate total shortening.
7. Click Calculate, then export CSV or PDF if needed.

For critical work, compare with project specifications and local codes.

Practical notes

• Lower RH and smaller V/S typically increase drying shrinkage demand.
• Early curing quality affects shrinkage; protect fresh concrete from drying.
• Use joints and reinforcement detailing to control cracking patterns.
• Shortening estimates help coordinate cladding, partitions, and tolerance plans.

Use these estimates to reduce cracking and callbacks significantly.

Technical article

1) Shrinkage mechanisms in concrete

Concrete shrinkage is a time-dependent volume reduction driven mainly by moisture loss and internal chemical changes. Drying shrinkage dominates for many structural elements, while autogenous shrinkage becomes significant in low water–cement mixes. Typical long-term drying shrinkage magnitudes often fall between 400 and 900 microstrain (µε), depending on environment, mix, and member size.

2) Why designers quantify shrinkage

Shrinkage strain creates tensile stress when movement is restrained by reinforcement, supports, subgrade friction, or adjacent pours. For a 10 m member, 600 µε corresponds to about 6 mm of shortening (ΔL ≈ ε·L). Quantifying this helps with joint spacing, crack control reinforcement, prestress losses, and serviceability tolerances.

3) Relative humidity and the humidity factor

Ambient relative humidity strongly influences drying potential. Lower humidity increases shrinkage demand and speeds development. The calculator applies a humidity factor kh derived from humidity in decimal form. For example, around 60% RH produces substantially higher kh than 85% RH, reflecting greater moisture gradient and drying.

4) Geometry through volume-to-surface ratio

Member size controls how fast moisture escapes. A smaller volume-to-surface ratio (V/S) means more exposed area per unit volume, leading to faster shrinkage development. Thin slabs, walls, and toppings commonly show earlier shrinkage cracking than massive footings. Shape factor ks refines this for non-prismatic or slender sections.

5) Mix strength and water content effects

Higher mean compressive strength at 28 days (fcm28) generally correlates with lower ultimate drying shrinkage and a slower rate parameter. Water content (w) drives paste volume and capillary porosity; higher w usually increases ultimate shrinkage. When detailed mix data is unavailable, the nominal option provides a conservative starting point.

6) Time development and drying start age

Shrinkage does not begin at casting in this model; it begins at the drying start age tc, typically the end of moist curing. Earlier drying (small tc) accelerates development and can raise early cracking risk. The time function uses a characteristic half-time τsh so you can compare 28, 90, and 365-day behavior consistently.

7) Construction detailing implications

Use the output strain (µε) to estimate movement per meter and total shortening for the member length you enter. This supports joint layout, rebar distribution, and compatibility checks with cladding, partitions, and embeds. For restrained elements, combine shrinkage with creep and temperature movement in serviceability review.

8) Mitigation and reporting practice

Common mitigation measures include longer wet curing, fogging or curing compounds, shrinkage-reducing admixtures, optimized aggregate grading, and timely saw-cut joints for slabs. Exportable CSV and PDF outputs help maintain traceable assumptions for submittals, coordination meetings, and quality documentation. Always verify with project specifications and applicable standards.

FAQs

1) What does microstrain (µε) mean here?

Microstrain is strain multiplied by one million. For example, 500 µε equals 0.000500 strain. Multiply strain by member length to estimate shortening, then convert meters to millimeters as needed.

2) Why do I need both t and tc?

t is the concrete age when you want results. tc is the age when drying begins, usually after curing ends. The model uses the duration (t−tc) to drive shrinkage development.

3) How should I estimate V/S for my member?

V/S is the member volume divided by the exposed drying surface area. Use only the surfaces exposed to drying. Thinner members yield smaller V/S values and typically show faster shrinkage development.

4) What if my mix water content is unknown?

Select the nominal ultimate shrinkage option. It applies a representative ultimate value so you can still estimate strain and shortening. Replace it with mix-based inputs when trial mix or supplier data becomes available.

5) Does this include temperature movement or creep?

No. The calculator targets shrinkage strain only. For full movement checks, combine shrinkage with thermal strain and consider creep, especially for restrained members or long-term deflection and prestress loss reviews.

6) Why can higher humidity reduce shrinkage?

Higher ambient humidity reduces moisture gradients and slows drying, lowering shrinkage demand. At very high humidity, drying shrinkage can be small, though autogenous effects may still matter in low water–cement mixes.

7) How should I use the results in joint spacing?

Use the mm/m output to estimate expected movement over panel lengths. Pair that with restraint conditions, reinforcement, slab thickness, and saw-cut timing to select practical joint spacing and reduce random cracking.