Formula and Method for the Charpy/Izod Impact Test
A pendulum impact test measures the energy a material absorbs when it fractures under a sudden, high-strain-rate blow rather than a slow, steady load. A hammer of known mass swings from a fixed release height, strikes and breaks a notched specimen at the bottom of its arc, then continues swinging up the far side. The height it fails to reach on the far side is a direct measure of the energy the specimen consumed while breaking: E = mgL(cosβ − cosα), where m is the hammer mass, L is the pendulum arm length (the radius from the pivot to the hammer's center of percussion), α is the release angle measured from the vertical rest position, and β is the rebound angle measured the same way.
How the calculation works
Before release, the hammer sits at angle α from the vertical rest position, giving it a height h₁ = L(1 − cos α) above the specimen. All of that potential energy converts to kinetic energy at the bottom of the swing, where the hammer strikes and breaks the specimen. Whatever energy remains carries the hammer up the far side to angle β, a height of h₂ = L(1 − cos β). The difference, mg(h₁ − h₂), is the energy the specimen absorbed — algebraically that simplifies to mgL(cosβ − cosα), which the calculator applies directly. Dividing that energy by the fractured cross-sectional area beneath the notch gives the impact (notch) toughness, an intensive property that lets you compare specimens of different sizes.
Common mistakes
- Angle reference confusion: both α and β are measured from the same vertical reference — the specimen's position at the bottom of the swing — not from horizontal and not from each other.
- Using the wrong length: the arm length L is the effective radius to the hammer's center of percussion, not the full pendulum length; testing-machine manuals usually list this radius next to the hammer's rated capacity.
- Forgetting to subtract the notch: toughness uses the remaining ligament area beneath the notch (commonly 80 mm² for a standard 55×10×10 mm bar with a 2 mm V-notch), not the full 10×10 mm cross-section.
- Reporting energy without temperature: Charpy energy for steels changes sharply near the ductile-to-brittle transition temperature, so a bare joule value without a stated test temperature is not comparable across labs.
Real-world applications
- Bridge, pressure-vessel, and structural steel codes specify a minimum Charpy V-notch energy at a minimum service temperature to guard against brittle fracture.
- Pipeline steel grades are qualified with a full Charpy energy-versus-temperature transition curve, not a single-point test.
- Polymer and composite impact ratings (often Izod-style) use the same pendulum-energy method to compare material toughness for enclosures and consumer products.
- Production quality control uses Charpy energy as a fast, low-cost proxy for fracture toughness where slower fracture-mechanics testing is impractical.
Frequently Asked Questions
What's the difference between the Charpy and Izod impact test?
Both use a swinging pendulum to fracture a notched bar and measure absorbed energy the same way, E = mgL(cosβ − cosα). The difference is specimen mounting: a Charpy specimen is a simple beam supported at both ends with the notch facing away from the hammer, while an Izod specimen is clamped vertically like a cantilever with the notch facing the hammer. This calculator's energy formula applies to either configuration.
Why is the rebound angle smaller for a tougher specimen?
A tougher specimen absorbs more of the hammer's kinetic energy while it fractures, leaving less energy to carry the hammer up the far side of its swing. A small rebound angle β close to the vertical rest position means high absorbed energy and a tough material; a rebound angle close to the release angle α means the specimen absorbed very little energy and failed in a brittle manner.
How do I convert impact energy to impact (notch) toughness?
Divide the absorbed energy (in joules) by the cross-sectional area at the fracture plane — the remaining ligament beneath the notch, not the full bar cross-section. For the standard 55 × 10 × 10 mm Charpy V-notch bar with an 80 mm² (0.8 cm²) ligament, toughness in J/cm² equals absorbed energy divided by 0.8.
What units does this calculator use, and how do I get ft·lbf?
All inputs are metric: mass in kilograms, pendulum arm length in meters, and angles in degrees measured from the vertical rest position where the specimen sits. The calculator reports absorbed energy in joules and automatically converts it to foot-pounds-force (1 J = 0.737562 ft·lbf) for labs and older standards that use US customary units.
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
| Barber / hair salon | 15–20% | On pre-discount total |
| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |