About Compressive Strength of Concrete Calculation
This concrete hardening calculator estimates the compressive strength of concrete at each curing stage, taking into account concrete age, average curing temperature, concrete strength class according to EN 206, and cement strength development class. The calculation shows the percentage of strength development, mean cylinder compressive strength, estimated characteristic and cube compressive strength, and the time remaining until the required structural strength level is reached.
The calculation is based on the concrete strength development model from EN 1992-1-1. Temperature is taken into account through the equivalent age of the concrete, so the same actual age can produce different results at different curing temperatures.
Guidelines and recommendations
Concrete class and design strength
Concrete class. The EN 206 designation contains two characteristic compressive strength values at 28 days. For example, for C25/30 the first value, 25 MPa, is the characteristic cylinder compressive strength, while the second value, 30 MPa, is the characteristic cube compressive strength.
The calculation uses concrete classes C8/10, C12/15, C16/20, C20/25, C25/30, C30/37, C35/45, C40/50, C45/55, C50/60, C55/67, C60/75, C70/85, C80/95, C90/105, and C100/115. For each class, the first value is taken as the characteristic cylinder compressive strength fck, and the second as the characteristic cube compressive strength.
Mean cylinder compressive strength. The reference mean strength at 28 days is determined from:
fcm = fck + 8 MPa
For example, for C25/30, fck = 25 MPa, so the mean cylinder compressive strength is fcm = 33 MPa.
Effect of curing temperature
Average concrete temperature. The calculation uses the average temperature of the concrete itself over the period being considered, in degrees Celsius. This temperature converts the actual age into a temperature-adjusted, or equivalent, concrete age.
The temperature factor is calculated as:
kT = exp(13.65 - 4000 / (273 + T))
where T is the average concrete temperature, °C. The equivalent age is then determined as:
tT = t × kT
where t is the actual age of the concrete in days. At 20 °C, the factor is close to 1.00, so the actual and equivalent ages are nearly the same. At lower temperatures, the equivalent age decreases, while at higher temperatures it increases.
Temperature assumption. The calculator uses one average temperature value for the entire specified period. The calculation range is limited to temperatures from 0 °C to 80 °C.
Strength development class
Rate of strength development. The EN 1992-1-1 model uses a coefficient s related to the cement strength class. The calculator uses three values:
s = 0.20- class R, rapid strength development, for CEM 42,5 R, CEM 52,5 N, and CEM 52,5 R.s = 0.25- class N, normal strength development, for CEM 32,5 R and CEM 42,5 N.s = 0.38- class S, slow strength development, for CEM 32,5 N.
A lower s value corresponds to faster early-age strength development. If class N is selected, the calculation uses a coefficient of 0.25.
Calculation of strength development
Strength development coefficient. After determining the equivalent age, the coefficient βcc is calculated:
βcc(t) = exp{s × [1 - √(28 / tT)]}
This coefficient indicates what proportion of the mean 28-day strength the concrete has reached under the specified curing conditions. In the calculator, its value is limited to a maximum of 1.00, so the displayed strength development does not exceed 100 %.
Strength development. The percentage is calculated directly from the strength development coefficient:
P = βcc(t) × 100 %
For example, βcc = 0.70 corresponds to 70 % strength development.
Mean and characteristic compressive strength
Mean cylinder compressive strength. The current compressive strength is calculated from the mean 28-day strength:
fcm(t) = βcc(t) × fcm
Therefore, for the same concrete class, the result changes depending on concrete age, curing temperature, and strength development class.
Characteristic cylinder compressive strength. For an equivalent age greater than 3 days but less than 28 days, the following relationship is used:
fck(t) = fcm(t) - 8 MPa
If the calculated value is below zero, 0 MPa is used. At an equivalent age of 28 days or more, the characteristic compressive strength is taken as the first value of the selected concrete class. At an equivalent age of up to 3 days, a numerical value of fck(t) is not calculated and strength verification by testing is required.
Cube compressive strength. For each concrete class, the second value in the EN 206 designation is used. The current estimated value is calculated in proportion to the strength development coefficient:
fcube(t) = βcc(t) × fcube,28
For example, for C25/30 the reference cube compressive strength is 30 MPa.
Time required to reach the target strength
Required strength level. The target strength development can be set from 1 % to 100 %. For example, 70 % means reaching a strength development coefficient of βcc = 0.70.
First, the equivalent age corresponding to the specified percentage is calculated from the strength development equation:
tT,target = 28 / [1 - ln(P / 100) / s]2
It is then converted to actual age using the temperature factor:
ttarget = tT,target / kT
The time already elapsed is subtracted from the calculated age. The result therefore shows the number of days remaining until the specified strength level is reached. If the calculated target age is less than or equal to the current concrete age, the required strength is considered to have already been reached.
European standards
EN 206 "Concrete. Specification, performance, production and conformity". This standard provides the concrete strength classes and the corresponding characteristic cylinder and cube compressive strength values used in the calculation.
EN 1992-1-1 "Eurocode 2. Design of concrete structures. Part 1-1: General rules and rules for buildings". The model used to calculate the development of mean compressive strength, the age-dependent relationship, and the coefficients for cement strength development classes are based on this standard.
EN 13670 "Execution of concrete structures". This standard specifies requirements for the execution of concrete structures and is used together with project documentation when assessing the actual condition of a concrete element.
FAQs
Why can concrete of the same age have different compressive strength?
The rate of concrete strength development depends not only on the number of days since placement, but also on concrete temperature and the cement strength development class. Therefore, concrete that is, for example, 5 days old can have a different equivalent age and different calculated compressive strength under different curing conditions.
What does 70 % concrete strength development mean?
It means that the calculated strength development coefficient has reached 0.70 relative to the mean strength used for the age of 28 days. A value of 70 % is often used as a convenient reference, but the required level should be selected according to the requirements of the specific project and construction procedure.
Why is the equivalent concrete age almost the same as the actual age at 20 °C?
In the temperature relationship used by the calculator, the factor kT is close to 1.00 at 20 °C. Therefore, one actual day of curing corresponds to approximately one equivalent day, while higher or lower temperatures accelerate or slow the calculated development of concrete strength.
What is the difference between cylinder and cube compressive strength?
They refer to compressive strength measured using specimens of different shapes, so their numerical values are different. In an EN 206 concrete class such as C25/30, 25 MPa is the characteristic cylinder compressive strength and 30 MPa is the characteristic cube compressive strength.
Why is fck(t) not shown for the first three equivalent days?
At a very early age, the relationship between characteristic and mean compressive strength is less reliable for direct numerical estimation. Therefore, at an equivalent age of up to 3 days, the calculator does not display a calculated fck(t) value and indicates that strength should be verified by testing.