Fatigue Life Calculator
Estimate fatigue life using S-N curve data and Miner rule for cumulative damage. Enter values for instant results with step-by-step formulas.
Calculator
Adjust values & calculateLoading Conditions
Material Properties
Marin Factors & Loading
Formula
The modified endurance limit Se is the fatigue strength adjusted by Marin surface (ka), size (kb), and reliability (kc) factors. The Goodman criterion converts mean+alternating stress to equivalent fully-reversed stress. Miner's rule accumulates damage as the ratio of applied to allowable cycles.
Last reviewed: December 2025
Worked Examples
Example 1: Steel Shaft Under Reversed Bending
Example 2: Cumulative Damage Assessment
Background & Theory
The Fatigue Life Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads โ the permanent self-weight of structural elements, finishes, and fixed equipment โ and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40โ0.45 typically yields concrete with 28-day compressive strengths of 30โ40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5โ2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250โ350 MPa for mild steel) and ultimate tensile strength (typically 400โ500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by ฮด = FLยณ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of mยฒยทK/W (SI) or ftยฒยทยฐFยทh/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1โ2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.
History
The history behind the Fatigue Life Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete โ a mixture of volcanic ash, lime, and seawater โ enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including Franรงois Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes โ including the 1971 San Fernando and 1994 Northridge events โ drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.
Frequently Asked Questions
Formula
Se = ka x kb x kc x Sf | Goodman: Sa/(1 - Sm/Su) | D = n/Nf
The modified endurance limit Se is the fatigue strength adjusted by Marin surface (ka), size (kb), and reliability (kc) factors. The Goodman criterion converts mean+alternating stress to equivalent fully-reversed stress. Miner's rule accumulates damage as the ratio of applied to allowable cycles.
Worked Examples
Example 1: Steel Shaft Under Reversed Bending
Problem: A machined steel shaft (Su = 500 MPa, Sf = 250 MPa) experiences 250 MPa alternating stress with 50 MPa mean stress. Surface factor 0.85, size factor 0.90, reliability 0.897. Estimate fatigue life.
Solution: Modified Se = 250 x 0.85 x 0.90 x 0.897 = 171.7 MPa\nGoodman equivalent = 250 / (1 - 50/500) = 277.8 MPa\nSince 277.8 > 171.7 MPa, finite life expected\nUsing S-N approach with slope from 0.9 x Su at 10^3 to Se at 10^6\nlog(450) = 2.653, log(171.7) = 2.235\nSlope m = (2.653 - 2.235) / (3 - 6) = -0.139\nFatigue life estimated from S-N relationship
Result: Finite life predicted | Goodman SF = 0.618 | Component operates above endurance limit
Example 2: Cumulative Damage Assessment
Problem: The same shaft has already experienced 100,000 load cycles. Assess remaining life using Miner's rule if S-N life is 500,000 cycles.
Solution: Applied cycles: 100,000\nS-N life at operating stress: 500,000 cycles\nDamage fraction D = 100,000 / 500,000 = 0.20 (20%)\nRemaining life = 1 - 0.20 = 0.80 (80%)\nRemaining cycles = 0.80 x 500,000 = 400,000 cycles
Result: Damage: 20% | Remaining life: 80% (400,000 cycles remaining)
Frequently Asked Questions
What is fatigue life and why is it important in engineering?
Fatigue life is the number of stress cycles a material or component can withstand before failure occurs due to progressive and localized structural damage from cyclic loading. Unlike static failure where a single overload causes fracture, fatigue failure occurs at stress levels well below the material's ultimate tensile strength or even yield strength. Fatigue is responsible for approximately 80 to 90 percent of all structural failures in engineering applications, making it the most critical failure mode in mechanical design. Components subject to repeated loading such as aircraft wings, bridge structures, engine crankshafts, turbine blades, and automotive suspension parts must be designed with fatigue considerations. The fatigue design process involves characterizing the loading spectrum, determining material fatigue properties from S-N curves, applying mean stress corrections, and incorporating safety factors to ensure reliable service life.
How does the S-N curve characterize material fatigue behavior?
The S-N curve (stress-life curve or Wohler curve) plots stress amplitude versus the number of cycles to failure on a log-log scale. It is the fundamental characterization tool for fatigue analysis. For ferrous metals like steel, the curve typically shows a distinct knee point around 10 to the sixth to 10 to the seventh cycles, below which the material theoretically has infinite life. This stress level is called the endurance limit or fatigue limit. For non-ferrous metals like aluminum and copper alloys, there is no true endurance limit and the curve continues to decrease. The S-N curve is obtained through rotating beam or axial fatigue testing of multiple specimens at different stress levels, recording cycles to failure. The high-cycle fatigue region (greater than 10 to the fourth cycles) is primarily elastic and stress-controlled, while low-cycle fatigue involves significant plastic deformation and is strain-controlled.
What is Miner's rule for cumulative fatigue damage?
Miner's rule, also known as the Palmgren-Miner linear damage accumulation rule, states that fatigue damage from different stress levels can be summed linearly. The damage fraction at each stress level equals the ratio of applied cycles to the cycles-to-failure at that stress level: D = sum of (ni / Nfi). Failure is predicted when the total damage D reaches 1.0 (100 percent). For example, if a component experiences 50,000 cycles at a stress level that would cause failure at 200,000 cycles, the damage is 0.25 or 25 percent, leaving 75 percent remaining life. While widely used for its simplicity, Miner's rule has known limitations: it does not account for load sequence effects (high-then-low versus low-then-high loading produces different results), it ignores crack initiation versus propagation differences, and experimental data shows failure at damage sums ranging from 0.7 to 2.2.
How accurate are the results from Fatigue Life Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
Can I use Fatigue Life Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
References
Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy