Engineers learn many types of equations and formulas that support their success in their career fields. From calculating force and strain to evaluating thermal radiation and even financial metrics, professionals in engineering rely on specific formulas when planning and developing products, systems and processes. If you’re considering a career in engineering, it’s important to develop your skills with common mathematical functions.
In this article, we explore what engineering formulas are and some of the equations you’re likely to encounter as an engineer.
What are engineering formulas?
Engineering formulas are mathematical computations professionals use to evaluate and understand the applications they design and build. Within engineering, you may encounter a variety of different formulas that are essential to solving technical challenges and ensuring projects are successful. Although formulas can be equations, there are some differences between them:
Equations
Equations by definition are mathematical statements that set two expressions equal to one another. Unlike formulas, though, equations often contain more known variables, which make them useful for many types of applications. Additionally, you can adjust equations more freely based on the inputs you use and you can apply these computations in any area of engineering that requires mathematical evaluation.
Formulas
A formula is a type of equation that follows a standard set of procedures to solve. When solving formulas, you’re generally solving for more unknown values that depend on certain parameters, such as constant and dependent variables. In addition, formulas represent a relationship between the variables you’re computing and are often specific to individual applications. For example, the formula for thermal convection is specific to heat transfer and cooling so a software engineer isn’t likely to use the computation in their work.
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11 common engineering formulas
Consider the following formulas that engineers apply across applications in mechanics, finance, aerospace, civil and structural designs:
1. Pythagorean theorem
The Pythagorean Theorem measures the hypotenuse of a right triangle to determine the diagonal length in relation to the 90-degree angle. The formula states that a² + b² = c², wherein you add the squares of the two sides forming the right angle (a² and b²) to get the squared diagonal measure (c²). This formula is common in civil and structural engineering, where architects, designers and builders can apply it to determine the diagonal length of various infrastructures, such as buildings, bridges and roadways.
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2. Law of relativity
Albert Einstein’s law of general relativity serves as a foundation for many mathematical applications in aerospace engineering and design. The formula states that the observational effects of gravity between masses arise from the masses’ warping of spacetime around it. This theory is instrumental for understanding how gravity and electromagnetism affect moving bodies in space, which many engineers who work in the aerospace sector rely on for testing and assuring the efficacy of their designs.
Within Einstein’s theory is a formula for calculating general relativity in relation to energy, mass and the speed at which light travels through space. The equation E = mc² represents the energy (e) a specific body exerts in space in the form of electromagnetism. You can determine this energy by multiplying the body’s mass (m) by the square of the speed of light (c), which is a constant value.
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3. Young’s modulus of elasticity
Young’s modulus measures the ability of a material to withstand lengthwise compression and tension that cause changes to the length of the material. This engineering concept relates to elasticity and equals the quotient between longitudinal stress and material strain. Many engineers apply this formula to complete construction projects and design and build machinery, equipment and sophisticated systems for manufacturing production.
Engineering professionals in the aerospace and defense industries may also work with Young’s modulus to determine viable designs for aircraft, mechanical components, spacecraft, satellites and military defense applications. The equation for Young’s modulus is E = σ / ε = (F/A) / (change in L / initial L) = (FL / A x change in L), where σ is the stress, ε is the strain, F is the force, A is the surface area of the material applying the force, L is the initial length and the change in L represents the positive or negative value of compression or extension on the material.
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4. Torque
Torque is an essential measurement many engineers and automotive design technicians apply when developing mechanical systems, parts and components. The torque of a system refers to the twisting force that causes rotation along an axis point. The formula for calculating torque is T = F x r x sin(θ), where F represents linear force, r represents the distance between the axis of rotation and point of force and theta (θ) is the angle between the force and point of rotation. This mathematical concept is integral to determining how centrifugal force affects objects in motion.
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5. Acceleration
Acceleration measures the change in velocity in relation to a change in time. The equation for acceleration is a = change in v / change in t, where v represents velocity and t stands for the time value. It allows engineers to evaluate how quickly velocity changes when substituting specific time values for the t variable. Engineers rely on computations involving acceleration and by relation velocity, in applications ranging from rocket mechanics and automotive design to scientific applications like climatology and environmental engineering.
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6. Velocity
The velocity of a moving object is a vector that measures the displacement in relation to a change in time and uses the equation v = change in s / change in t. The change in s represents the speed at which an object is moving, while the change in t is the ratio between the initial time and the time value at the moment you measure it. Similar to acceleration, velocity is a scientific and mathematical concept that engineers take into account when designing different mechanical systems, such as cars, aircraft and military defense equipment.
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7. Force
Force represents one of Isaac Newton’s laws of motion and measures the force an object exerts in relation to the object’s mass and rate of acceleration. To calculate force, you can use the equation F = m x a, where the mass of an object (m) multiplies by the acceleration (a) to exert force (F). This formula is another important computation that engineering professionals can use to determine how much force an object puts out at different rates of acceleration.
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8. Stress
Stress measures the internal force of an object in relation to a cross-sectional area in which the object resides. Measuring the stress point of a structure is critical to the integrity of many types of constructions, including buildings, bridges, roads and mechanical systems and components. Engineers evaluate stress using the formula s = F/A, where s is the stress value, F is the force and A represents the cross-sectional surface area. Additionally, understanding stress is critical to evaluating the maximum load a material can withstand before breaking.
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9. Compound interest
Compound interest can be a crucial metric to calculate in sales engineering, logistics and supply chain management. While compound interest is typically only applicable in financial situations, economists and data engineers may also apply this formula when making cost projections, analyzing economic data and making financial decisions that impact entire organizations.
To calculate compound interest, you can use the formula P (1 + r/n)(nt) – P, where P is your principal, r is the interest rate, n is the number of times you compound the interest each period and t represents the time in years you apply the compound interest. To calculate the future value of the principal, you can use the formula A = P (1 + r/n)(nt).
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10. Heat loss
Heat loss describes the rate at which an object cools and can occur through thermal radiation or through conduction. While thermal convection measures the rate of heat transfer between areas, thermal radiation and conduction describe the process of rapid cooling. Professionals in mechanics, aviation, aerospace, chemical and nuclear engineering may apply heat loss formulas regularly when completing design projects, as many of these types of applications rely on the evaluation of heat loss and energy transference. The formula for heat loss through thermal radiation is p = eoA(T⁴ – Tc⁴).
In this formula, p represents the net radiation of an object, e represents the object’s emissivity, o is the constant of the Stefan-Boltzman law, T is the temperature of the radiating object and Tc represents the surrounding temperature. Heat loss through thermal conduction uses the formula Q/t = [kA(T2 – T1)] / d, where Q is the amount of heat transferring over time (t) and equal to an object’s thermal conductivity over a surface area (A) in relation to the difference between the temperature on one side of the object (T1) and the temperature on the other (T2).
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11. Thermal convection
Thermal convection refers to a method of heat transfer, in addition to radiation and conduction. It measures the transfer of thermal energy between locations in relation to the movement of fluids, such as liquids, plasmas or gases. Many engineers working with fluid dynamics, such as aeronautical engineers, rely on the laws of heat transfer to evaluate propellants and viable sources of propulsion for aircraft like jets, rockets and even missiles.
The formula for calculating heat transfer through thermal convection is q = hcA dT, where you multiply the coefficient of convective heat transfer (hc), the heat transfer area on the surface (A) and the difference in temperature between the fluid and the surface.