Compression test: what it is, how to calculate it, concrete (NBR 5739 and fck) and standards

The compression test applies an increasing axial force to shorten a test specimen and measure its strength and deformation. Compressive strength is the maximum force divided by the original cross-sectional area, σ = F / A₀, in MPa. For concrete, under ABNT NBR 5739:2018 (the Brazilian standard for compression testing of concrete cylinders), f_c = 4F / (πD²): a 10 × 20 cm cylinder that fails at 236 kN has 30.0 MPa.

It is the test that approves the concrete on a construction site, measures the compressive yield of metals and qualifies plastics, foams, wood, springs and packaging. This guide covers what the test measures, the test specimen, the curve of each type of material, the formulas, the NBR 5739 procedure step by step, what fck is and how to calculate it, compression testing of other materials, solved exercises, the standards and how to choose the machine.

The photo shows a concrete cylinder broken between the platens of the press: the inclined cracks form cones, the typical failure pattern of concrete in this test.

What is a compression test

In a compression test, the specimen sits between two parallel platens, and the machine moves them together at a controlled rate. Force and shortening are recorded until failure or until a deformation limit set by the standard. It is the opposite of the tensile test, which pulls the specimen apart, and it is one of the basic mechanical tests.

The force and shortening records give the mechanical properties of the material in compression:

• Compressive strength: the highest stress the material withstands before failing, that is, the maximum force divided by the original area, in MPa. Because it is a stress and not a force, it allows specimens of different sizes to be compared.
• Compressive yield strength: the stress at which permanent deformation begins. This is the value reported for ductile metals.
• Modulus of elasticity: the slope of the initial straight portion of the curve. It measures stiffness: the higher the modulus, the less the material shortens under the same stress.
• Elastic and plastic deformation: elastic deformation disappears when the load is removed; plastic deformation remains. The curve shows where one ends and the other begins.
• Failure mode: whether the specimen fails in cones, along an inclined plane, by shattering, or simply flattens. In concrete, the failure type is part of the result and points to preparation defects.

These values are used to design columns, foundations and compression members, to choose between materials, to control the quality of batches and to follow the development of new formulations. The test also measures how temperature, moisture or aging change strength, and it is used to validate numerical models, such as finite element models, by comparing the measured curve with the calculated one. It is a destructive test: the specimen comes out broken or crushed, so it is taken from a representative sample of the batch.

Compressive strength only makes sense for materials that fail at a clear force peak, such as concrete, cast iron and ceramics, which are brittle. Ductile metals do not fracture in compression: they flatten and barrel, that is, they shorten and bulge in the middle, taking a barrel shape. For these, ASTM E9 requires reporting the compressive yield strength or the stress at a specified strain, because a "strength" would depend only on how far the specimen was crushed. The two diagrams below show this difference: on the left, the specimen that shortens and widens, with the initial and final heights and diameters; on the right, the brittle material that fractures along an inclined plane between the platens.

Test specimen for compression testing

The test specimen is a sample with a shape and dimensions set by the material standard, so that different laboratories reach comparable results. The cylinder is the most common shape; plastics, wood and foams also use prisms and cubes. Three precautions apply to all of them:

• Height-to-diameter ratio (h/d). A tall, slender specimen tends to buckle, that is, to bend sideways before failing in compression. A very short specimen is more affected by friction with the platens, which prevents the end faces from expanding, and it fails at a higher force than the material actually withstands. That is why each standard sets the h/d: for concrete it is 2, and shorter specimens have their force corrected.
• Flat, parallel end faces perpendicular to the axis. Otherwise the load concentrates on one side and the specimen fails early. The faces are machined or ground; for concrete, capping (a thin layer that levels the face) or an unbonded neoprene pad is also used.
• Measured dimensions, not nominal ones. The area used in the calculation comes from the diameter or sides measured on the specimen itself.

The specimen must be free of cracks, voids and burrs, and it is identified with the material, the batch and the age or test condition. The dimensions required by each standard are given in the sections on concrete and on other materials, further on.

Stress-strain curve in compression

During the test, the software divides the force by the original area and the shortening by the original height and plots the stress-strain curve. Each class of material produces a curve of a different shape, and that shape decides what is reported. The graph below compares three cases: the ductile metal, whose curve rises without a peak because it flattens without breaking; concrete, which is brittle, reaches a peak and drops when it fails; and rigid foam, which forms a plateau after the elastic portion while the cells collapse.

In metals, the initial portion is straight, as in tension, and yield is read by the 0.2% offset method, explained in "How to calculate" just below. In concrete and other brittle materials, the value of interest is the peak. In foam, which often has no peak, the stress at a fixed strain is reported. The table summarizes, material by material, how it deforms and fails, what is reported and the standard:

Material	How it deforms and fails	What is reported	Standard
Ductile metals (steel, aluminum, copper)	barrels, does not fracture	0.2% yield strength, modulus, curve	ASTM E9
Gray cast iron	shear fracture along an inclined plane	maximum strength	ASTM E9
Concrete	cones and shear (types A to G)	fc and the batch fck	ABNT NBR 5739
Technical ceramics	shattering	maximum strength	ASTM C773 (whiteware ceramics)
Rigid plastics	yielding or crushing	strength, yield and modulus	ASTM D695, ISO 604
Rigid foams	cell collapse	stress at 10% strain	ISO 844, ASTM D1621
Wood	fiber crushing	fc0 parallel to the grain, at 12% moisture content	ABNT NBR 7190-3 (Brazilian timber test standard)

Why metals barrel. Friction with the platens keeps the end faces from expanding, while the middle of the specimen widens freely. The effect increases the apparent force; it is reduced with a lubricant on the faces (PTFE or paraffin) and with the height-to-diameter ratio set by the standard. The photo below shows the result on an aluminum cylinder: on the left, the original specimen; on the right, the same specimen after compression, shorter, wider in the middle and without a single crack.

Why brittle materials fail at an angle. In uniaxial compression, the maximum shear stress acts on planes at about 45° to the axis. Friction with the platens changes this angle, and in concrete it produces the characteristic cones.

Why concrete and cast iron are stronger in compression than in tension. Microcracks and graphite flakes open cracks when pulled and tend to close when compressed. Class 30 gray cast iron has about 752 MPa in compression versus 207 MPa in tension; alumina, about 2,100 MPa in compression versus 345 MPa in flexure; a concrete with 30 MPa compressive strength has a mean tensile strength of only 2.9 MPa according to ABNT NBR 6118 (the Brazilian code for the design of concrete structures), close to 10% of that.

How to calculate compressive strength

The calculation follows the same logic as in tension: stress is the force divided by the original area, and strain is the shortening divided by the original height. The modulus of elasticity requires measuring the shortening on the specimen itself, with a compressometer, which is an extensometer set up for compression; the platen displacement includes the deformation of the machine and would give a modulus lower than the real one. The table gathers the formulas:

Quantity	Formula	Unit and note
Compressive stress	σ = F / A0	MPa (N/mm²); A0 is the original area
Strength of a concrete cylinder	fc = 4F / (π·D²)	MPa, to 3 significant figures (NBR 5739)
Strain	ε = ΔL / L0	shortening over the original height
Modulus of elasticity in compression	E = Δσ / Δε in the linear portion	GPa; requires a compressometer or extensometer
Compressive yield strength (metals)	0.2% offset, as in tension	MPa (ASTM E9)

Offset yield is read by drawing a line parallel to the straight portion of the curve, shifted 0.2% along the strain axis: where it crosses the curve is the yield strength. The fck formulas, which deal with the set of results from a batch of concrete, are in the section on fck, further on.

Example. A concrete specimen with a mean diameter of 100.2 mm failed at 248.6 kN at 28 days. The area is π × 100.2² / 4 = 7,885 mm², so f_c = 248,600 / 7,885 = 31.5 MPa.

Concrete compression test: NBR 5739 step by step

ABNT NBR 5739:2018 is the Brazilian standard for testing cylindrical concrete specimens molded according to NBR 5738, and cores, which are cylinders drilled from the finished structure according to NBR 7680-1. On site, specimens are molded from the delivered concrete, cured and broken at a defined age, and each result goes into the batch control, covered in the section on fck. This control works with samples: under NBR 12655 (the Brazilian standard for concrete preparation, control and acceptance), each sample consists of two specimens from the same batch, tested at the same age, and the higher of the two results counts.

1. Test specimen. A 10 × 20 cm or 15 × 30 cm cylinder, molded according to NBR 5738. The height-to-diameter ratio can never exceed 2.06; below 1.94, the force is corrected (table right after the steps).
2. Curing. Moist or saturated until the test age: in a moist room at 23 ± 2 °C with humidity above 95%, or in a saturated calcium hydroxide solution, after at least 24 h in the molds.
3. End preparation. Grinding, capping or an unbonded device (neoprene). Poorly prepared ends cause type F and G failures.
4. Dimensions. Caliper with 0.1 mm resolution; diameter as the mean of two perpendicular measurements at mid-height.
5. Age. The reference is 28 days, with a tolerance of ± 24 h. Specimens are also tested at 24 h (± 0.5 h), 3 days (± 2 h), 7 days (± 6 h), 63 days (± 36 h) and 91 days (± 48 h).
6. Machine. Calibrated to ISO 7500-1 (ABNT NBR ISO 7500-1 in Brazil) at least every 12 months, with a range such that failure falls within the calibrated interval. The specimen is centered on the platen.
7. Loading. Continuous and without shock, at 0.45 ± 0.15 MPa/s, which gives about 3.5 kN/s for the 10 × 20 and 8.0 kN/s for the 15 × 30. Loading stops only when the force drop indicates failure.
8. Calculation. f_c = 4F / (πD²), in MPa, to three significant figures.
9. Failure type. Record the type, from A to G.

The correction compensates for the effect described in the section on the test specimen: a shorter cylinder fails at a higher force. The factor reduces the measured force to what a cylinder with h/d = 2 would have given:

h/d	2.00	1.75	1.50	1.25	1.00
Force correction factor (NBR 5739, Table 2)	1.00	0.98	0.96	0.93	0.86

Failure types (Annex A of NBR 5739). A: conical, and conical with the cone 25 mm away from the cap. B: conical and split, or conical with more than one split. C: columnar with cone formation. D: conical and sheared. E: sheared. F: fractures at the top or bottom, below the cap. G: similar to F, with fractures near the top. When the specimens of a single sample show high scatter, the failure is usually type F or G, a sign of a molding or end-preparation defect.

In the United States, ASTM C39 applies, with a loading rate of 0.25 ± 0.05 MPa/s, about half the Brazilian rate. Results obtained under the two standards should not be compared without care.

fck: what it is, formula and what fck 30 MPa means

Three symbols are easily confused. f_c is the result of a single test specimen. f_cm is the mean of the results. f_ck is the characteristic strength: the value with a 95 % probability of being exceeded at 28 days. The difference between the mean and fck depends on how much the results vary, measured by the standard deviation s_d; the 1.65 in the formulas is the 5 % quantile of the normal distribution.

• In mix design (NBR 12655, the Brazilian standard for concrete preparation, control and acceptance): f_cm = f_ck + 1.65·s_d. With no history, the standard deviation is set by the preparation condition: 4.0 MPa (A), 5.5 MPa (B) or 7.0 MPa (C). For fck 30 MPa, the target mean is 36.6, 39.1 or 41.6 MPa.
• In lot control (20 or more samples): f_ck,est = f_cm − 1.65·s_d. The lot is accepted if f_ck,est ≥ f_ck.
• fck 30 MPa means the concrete was specified so that no more than 5 % of the 28-day results fall below 30 MPa.

The chart below shows this distribution for an fck 30 MPa concrete designed under condition A: the results are distributed around the mean of 36.6 MPa, and only the 5 % tail falls below 30 MPa.

The most common mistake is comparing the mean with fck. A lot of 24 samples with a mean of 34.0 MPa and a standard deviation of 2.5 MPa has f_ck,est = 34.0 − 1.65 × 2.5 = 29.9 MPa: it does not meet an fck of 30 MPa, even though the mean is 4 MPa higher. fck also names the strength classes: under NBR 8953 (the Brazilian standard for concrete strength classes), the number after the C is the fck in MPa, and group I classes range from C10 to C50. C20 is the minimum for reinforced concrete and C25 for prestressed concrete, under NBR 6118 (the Brazilian standard for the design of concrete structures). Try the numbers in the calculator below.

Compression testing of metals, plastics, ceramics and other materials

Outside concrete, the standard, the test specimen and what is reported change with the material.

Metals (ASTM E9). The test is used on structural steel, aluminum and titanium alloys, among others. The standard provides short, medium and long cylindrical specimens; to measure the strength of high-strength materials, the best length-to-diameter ratios are 1.5 and 2.0. The risks are buckling, in a slender or misaligned specimen, and barreling. A spherically seated upper platen, which tilts to follow the specimen face, compensates for small lack of parallelism. Structural steel has a compressive yield strength practically equal to its tensile yield strength, 250 to 500 MPa in common steels.

Plastics (ASTM D695 and ISO 604). D695 uses a 12.7 × 12.7 × 25.4 mm prism or a 12.7 × 25.4 mm cylinder at 1.3 mm/min; ISO 604 uses 10 × 10 × 4 mm. The two do not give comparable numbers, because geometry and speed differ. As in tension, the result for plastics depends on temperature and humidity, and the specimen is conditioned before the test.

Ceramics. Alumina, silicon nitride and other technical ceramics fail all at once, shattering, with no plastic deformation, and the maximum strength is reported. Since any misalignment concentrates stress in a material that does not yield to relieve it, face parallelism is critical. In porous ceramics, used in filters and catalyst supports, strength drops as porosity increases.

Composites. In carbon or glass fiber composites, compressive strength depends on fiber direction, so the test is performed in the directions that matter for the design. Thin specimens tend to buckle, and the result also changes with temperature and humidity.

Rigid foams (ISO 844, ASTM D1621 and EN ISO 29469, which replaced EN 826). Since many have no peak, the standard requires reporting the stress at 10 % strain. EPS insulation falls in the range of 100 to 500 kPa, depending on density.

Wood (ABNT NBR 7190-3, the Brazilian standard for timber testing). Strength parallel to the grain is measured at 12 % moisture content; in species used in structures, it is typically between 30 and 70 MPa.

Components. Springs, packaging, corrugated board and plastic pipes are also tested in compression, with platens, measuring force at a defined displacement. Corrugated board and boxes have their own tests (ECT, FCT, RCT and BCT), covered in the article on the crush test; flexible mattress and seat foams are evaluated by indentation force, in the IFD test.

Unconfined compression and triaxial testing of soils are a different family of tests, with their own standards; see triaxial test.

Axial compression and diametral compression

In axial compression, the cylinder stands upright and compressive strength is measured (NBR 5739). In diametral compression, the "Brazilian test" of ABNT NBR 7222:2011 (equivalent to ASTM C496), the cylinder lies on its side and the load along a generatrix produces tension on the diametral plane: f_ct,sp = 2F / (π·d·L), at 0.05 ± 0.02 MPa/s. A 10 × 20 C30 concrete cylinder that breaks lying down at 100 kN has 3.18 MPa of indirect tensile strength; standing upright, it would need 236 kN to reach 30 MPa.

Solved compression test exercises

1. Core with low h/d. A core 100 mm in diameter and 175 mm high (h/d = 1.75) failed at 200 kN. Since h/d < 1.94, the force is multiplied by 0.98: 196.0 kN. f_c = 4 × 196,000 / (π × 100²) = 25.0 MPa. Without the correction, it would be 25.5 MPa.

2. Mix design. For fck = 30 MPa under condition B (s_d = 5.5 MPa): f_cm = 30 + 1.65 × 5.5 = 39.1 MPa.

3. Metal, ASTM E9. Steel specimen of 12.7 × 25.4 mm (A₀ = 126.7 mm²). In the linear region, the force went from 5 kN to 25 kN while the compressometer read from 0.000197 to 0.000986 strain. Stresses: 39.5 and 197.3 MPa. E = (197.3 − 39.5) / (0.000986 − 0.000197) ≈ 200 GPa. The 0.2 % offset yield occurred at 40.0 kN: σ_e = 40,000 / 126.7 = 316 MPa. As the test continues, the specimen barrels and the force rises with no peak.

4. Machine capacity. A lab breaks 15 × 30 cylinders up to C40, with a mix design mean of 46.6 MPa. The expected force is 46.6 × 17,671 mm² = 823 kN. A 600 kN machine will not do; a 1,000 kN one will. For the 10 × 20 cylinder of the same class, the force is 366 kN, and 600 kN is more than enough.

Common mistakes in the compression test

1. Citing the old NBR 5739. The current edition is from 2018.
2. Non-parallel or poorly prepared ends. They concentrate stress and produce type F and G fractures.
3. Off-center specimen. It causes bending and lowers the result.
4. Wrong loading rate. Loading too fast overestimates strength.
5. Forgetting the h/d correction below 1.94, or testing above 2.06.
6. Age outside the tolerance (28 days ± 24 h).
7. Confusing f_c, f_cm and f_ck. Comparing the mean with fck accepts lots that do not comply.
8. Confusing slump with strength. "Slump 12 ± 2" is the slump of fresh concrete, 100 to 140 mm: it measures consistency, not strength.
9. Reporting the "ultimate strength" of a ductile metal. It does not exist: the yield strength is reported.
10. Measuring the modulus from platen displacement. It includes machine deformation and underestimates the modulus.

Compression test standards

The standard depends on the material and, for concrete, also on the stage: molding, testing, lot control and classification each have their own standards. The table lists the most widely used:

Standard	Application	Edition
ABNT NBR 5739	concrete, cylindrical specimens	2018
ABNT NBR 5738	molding and curing of specimens	2015
ABNT NBR 12655	preparation, control and acceptance of concrete (fck)	2022
ABNT NBR 8953	concrete strength classes	2015
ABNT NBR 7680-1	cores drilled from the structure	2015
ABNT NBR 7222	splitting tensile strength (diametral compression)	2011
ASTM C39/C39M	concrete (USA)
ASTM E9	metals	E9-19 (reapproved 2025)
ASTM D695 and ISO 604	rigid plastics	ISO 604:2002
ISO 844, ASTM D1621, EN ISO 29469	rigid foams (EN ISO 29469:2022 replaced EN 826, withdrawn)	ISO 844:2026
ABNT NBR 7190-3	wood	2022
ABNT NBR ISO 7500-1	machine calibration (ISO 7500-1)	2023

Compression testing machine: press or universal testing machine

The compression press is dedicated: high capacity and compression only, ideal for routine concrete testing. The universal testing machine with compression platens also performs tensile, flexural and shear tests, with speed control and extensometry, and is the choice for labs that also test steel, plastics or wood.

In both cases the parts are the same: a rigid frame, which must not deform along with the specimen; the drive system that brings the platens together at a controlled speed; the load cell, which measures force; strain measurement, by a compressometer on the specimen or by corrected crosshead displacement; and the software, which controls the test, plots the curve and issues the report. The Biopdi universal testing machine is electromechanical: a motor drives the screws that move the crosshead.

The capacity must cover the actual mean of the lot with margin, not just the fck, and specimen size matters as much as the class: the 10 × 20 cylinder requires about 44 % of the force of the 15 × 30 for the same strength. The chart below shows the force that breaks both cylinders in each class, from C20 to C50, compared with capacities of 300, 600 and 1,000 kN.

The panel below shows the universal testing machine, the role of each part in the compression test and the platens used.

The table links each application to the force range and the Biopdi equipment:

Compression application	Range	Biopdi equipment
Foams, small springs, light packaging	200 N to 10 kN	MBIOI-1P-M2 and MBIOI-10-M2
Plastics (D695), wood, small metal parts	5 to 50 kN	MBIOII-50-M2
Concrete 10 × 20 up to C25 (at C30, only the mean fits)	300 kN	MBIOII-300-M2
Concrete 10 × 20 up to C50; 15 × 30 up to about C30	600 kN	MBIOII-600-M2
Concrete 15 × 30 of high classes	1,000 kN	MBIOII-1000-M2
Dedicated routine compression testing	on request	Electric and hydraulic concrete compression testing machine

Operating details in universal testing machine. For soils, Biopdi offers the CBR and Marshall test press.

Compression test videos

Compression tests on Biopdi universal testing machines, including spring compression on the portable version.