The impact toughness calculator above turns a pendulum impact test into two numbers that are easy to confuse: the energy the specimen absorbed, in joules, and the toughness per unit of fractured area, in kilojoules per square metre. The first is what the machine reads out and what a material specification usually quotes. The second is what lets you compare a full-size bar against a subsize one, and it is the number that gets quietly dropped when people compare test results from two different laboratories.
Arb Digital publishes free engineering calculators that state their assumptions rather than hiding them behind a single output box. This page implements the standard pendulum energy balance, exposes every quantity that feeds it, and is explicit about what a Charpy or Izod result can and cannot be used for. It is a teaching and checking tool, not a substitute for a calibrated machine tested to a published standard.
What This Impact Toughness Calculator Does
A pendulum impact test is a controlled energy measurement. A heavy hammer is raised to a known angle, released, and allowed to swing through a notched specimen clamped at the bottom of its arc. Some of the pendulum's energy goes into breaking the bar, so it does not rise as high on the far side. The difference in height, multiplied by the weight of the pendulum, is the energy the specimen absorbed.
The tool computes that difference from your release and swing-up angles, or accepts the machine reading directly if you would rather start there. It then divides the energy by the fracture ligament area, which is the specimen depth minus the notch depth, multiplied by the specimen width. A standard 10 mm square Charpy V-notch bar with a 2 mm notch leaves 80 mm².
The hero figure is absorbed energy. The supporting grid gives toughness in kilojoules per square metre, the same figure in the older J/cm² convention still used across much of Europe, the energy in foot-pounds force for American specifications, and the ligament area itself so you can see exactly what the division used.
How to Use It
- Pick your input route. If you have a dial or digital reading, choose the direct mode and enter it in whatever unit the machine displays. If you are working from geometry, enter the pendulum's effective mass and arm length.
- Measure both angles from vertical. The release angle and the swing-up angle are both taken from the hanging position, not from horizontal. Mixing the two conventions is the most common arithmetic error in this calculation.
- Set the specimen geometry. The preset fills standard dimensions. If you tested a subsize bar because the stock was too thin for a full-size one, change the depth and the toughness will follow.
- Read the ligament area. Check it against what you physically measured on the broken halves. If it disagrees, the notch was not cut to the depth you assumed and the toughness figure is wrong even though the energy figure is right.
- Repeat across temperature. A single result at one temperature tells you very little. The value of impact testing is the shape of the curve as temperature falls.
The Formula: How Impact Energy Is Calculated
The pendulum's potential energy at the release angle is m g L(1 − cos α), where m is the effective mass, L is the distance from the pivot to the centre of mass, and α is the release angle measured from vertical. After breaking the specimen it rises to angle β, retaining m g L(1 − cos β). Subtracting one from the other, the absorbed energy is E = m g L(cos β − cos α). The tool uses the standard gravitational acceleration of 9.80665 m/s², the value fixed by the NIST Office of Weights and Measures for the conventional international system.
Notch toughness is then ak = E ÷ A, where A = (W − notch depth) × B. Expressed in SI that gives joules per square metre, and because the numbers are large the tool reports kilojoules per square metre.
Work the defaults through by hand. A 20 kg pendulum on a 0.75 m arm released at 140° and rising to 95° gives cos 95° − cos 140° = −0.08716 + 0.76604 = 0.67889. Multiply by 20 × 9.80665 × 0.75 = 147.100 and the absorbed energy is 99.86 J, or 73.66 ft·lbf. The ligament is 8 × 10 = 80 mm² = 80 × 10−6 m², so the toughness is 99.86 ÷ 0.00008 = 1,248,000 J/m², which is 1,248 kJ/m² or 124.8 J/cm². The same pendulum released at 140° carries 259.8 J of available capacity, so this specimen consumed about 38 per cent of it.
Why the Number Is Comparative and Not a Material Property
A Charpy result depends on the notch root radius, the specimen size, the striker geometry, the impact velocity and the temperature. Change any one of them and the number changes, even though the steel has not. That is why the standards are so prescriptive about dimensions: the test only means anything when every laboratory does the identical thing to an identical bar. ASTM E23, Standard Test Methods for Notched Bar Impact Testing of Metallic Materials, and ISO 148-1, Metallic materials — Charpy pendulum impact test, are the two documents that define those geometries, and a result quoted without naming one of them is close to meaningless.
This matters most when someone tries to use an impact energy in a calculation. It cannot go into a stress equation. It is not fracture toughness in the fracture-mechanics sense, it has different units, and it does not scale into a critical crack size. If you need a value you can compute a defect tolerance from, you need a plane-strain fracture toughness measured on a fatigue-precracked specimen, which is an entirely different and far more expensive test.
The Ductile-to-Brittle Transition Is the Real Output
Body-centred cubic metals, which include most ferritic and carbon steels, absorb a lot of energy when warm and very little when cold, with a fairly narrow transition between the two. A steel that gives 200 J at room temperature can give 15 J at −40 °C. Structures fail at the cold end, so the whole reason the test exists is to locate that transition and confirm it sits below the lowest service temperature.
This is why testing at a single convenient temperature wastes the test. Standard practice is a series of specimens across a temperature range, plotted as energy against temperature, with the transition defined either by a nominated energy such as 27 J or by the percentage of shear on the fracture face. Face-centred cubic metals such as austenitic stainless steels and aluminium alloys have no sharp transition at all, which is exactly why they are chosen for cryogenic work.
Where the Energy Actually Goes
Not all of the absorbed energy breaks the specimen. Some goes into throwing the two halves clear, some into friction at the pivot and windage, and some into elastic vibration of the machine. Calibrated machines are checked against certified reference specimens precisely because those losses are not negligible. The NIST Charpy Machine Verification Program exists to supply those reference specimens and to keep machines in different laboratories reading consistently.
The practical consequence is that a machine reading and a geometry calculation will not agree exactly, and the geometry calculation is the one to distrust. If you compute a much larger energy from your angles than the dial shows, you have probably used the striker radius instead of the centre of percussion distance, or the total pendulum mass instead of its effective mass.
The specimen should also absorb between roughly 10 and 80 per cent of the machine's capacity. A very tough bar on a small machine may not break at all; a brittle one on a large machine gives a reading buried in friction noise.
How This Sits Next to the Other Mechanical Tools
This page answers "how much energy did this notched bar absorb before it broke". It is not the same question as the impact force calculator, which computes an average force and deceleration from a mass, a speed and a stopping distance — that one is about collisions, this one is about a standardised material acceptance test. For elastic behaviour before anything fractures, the Young's modulus calculator and the stress strain calculator handle stiffness and the stress-strain relationship, while the hardness conversion calculator covers the other common comparative material test. The underlying energy accounting is the same conservative-force bookkeeping described in the OpenStax University Physics chapter on conservative and non-conservative forces.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Measuring angles from horizontal — the energy balance uses angles from the vertical hanging position, and swapping the convention changes the answer completely.
- Dividing by the full cross-section — the toughness denominator is the remaining ligament behind the notch, not the 100 mm² outer face of the bar.
- Comparing subsize and full-size results as energies — a 7.5 mm bar absorbs less energy simply because there is less of it, and only the per-area figure is comparable.
- Treating impact energy as fracture toughness — it has different units, a different specimen and a different purpose, and it cannot be used to compute a critical flaw size.
- Reporting one specimen — scatter near the transition temperature is large, and published specifications require a set of three for that reason.
Related Free Tools From Arb Digital
Use the stress strain calculator and the Young's modulus calculator for the elastic region that precedes any fracture, and the hardness conversion calculator when you need to move between Rockwell, Brinell and Vickers scales on the same material. The impact force calculator covers collisions rather than notched-bar testing, the energy converter moves between joules, foot-pounds and calories, and the temperature converter helps when a specification quotes a transition temperature in a unit you do not work in. Everything Arb Digital publishes is on the free online tools hub.
Frequently Asked Questions
Impact energy is the total energy in joules that the specimen absorbed, which is what the machine displays. Impact toughness is that energy divided by the fractured ligament area, giving kilojoules per square metre. Energy depends on how much material was there; toughness normalises for it, which is the only way to compare a full-size bar against a subsize one.
Because the notch removes material before the test starts. A standard 10 by 10 mm Charpy bar with a 2 mm V-notch fractures across the remaining 8 by 10 mm, so the area is 80 square millimetres and not 100. Dividing by the full face understates the toughness by 20 per cent.
No. It is a comparative acceptance test, not a design allowable. It is strongly sensitive to notch geometry, specimen size, striker shape and impact speed, and it has neither the units nor the theoretical basis to give a critical crack size. Defect tolerance work needs a plane-strain fracture toughness measured on a fatigue-precracked specimen.
It is the temperature range over which a body-centred cubic metal such as a carbon steel switches from absorbing a lot of energy to absorbing very little. The transition is why the test exists. A single result at room temperature says almost nothing; a curve of energy against temperature shows whether the transition sits safely below the lowest service temperature.
Usually because the effective mass or the arm length is wrong. The arm length must run from the pivot to the centre of percussion, not to the striker tip, and the mass is the machine's effective pendulum mass from its calibration certificate. Genuine friction, windage and specimen-toss losses also mean the two will never match exactly.
The specimen is supported differently. A Charpy bar rests horizontally on two anvils and is struck behind the notch as a simply supported beam. An Izod bar is clamped vertically as a cantilever and struck on the free end above the notch. Both measure absorbed energy the same way, but the results are not interchangeable.
Published test standards normally call for a set of three at each temperature, with both the average and the lowest individual value reported. Scatter near the transition is genuinely large, and a single specimen can fall well away from the set average without anything being wrong with the material or the machine.
This tool is provided for educational and preliminary engineering use. Impact testing is governed by published standards such as ASTM E23 and ISO 148-1, which specify specimen dimensions, striker geometry, temperature control and machine verification; results obtained outside those conditions are not comparable to certified values. Material acceptance decisions belong with a qualified metallurgist working from a calibrated machine and the governing specification.
