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Formulas and equations
Clear, worked formula pages that pair with the Formula Factory calculators. Each page shows the equation, what every symbol means, how to rearrange it to solve for any variable, a worked example, and the units involved — then links to the calculator that does the math for you. Free and printable.
📐 Physics 25
Area Moment of Inertia FormulaHome » Formulas & EquationsCALCULATOR Area moment of inertia formula The area moment of inertia describes how a cross-section resists […]Beam Deflection FormulaHome » Formulas & EquationsCALCULATOR Beam deflection formula Beam deflection is how far a loaded beam sags. For a simply […]Bearing Stress FormulaHome » Formulas & EquationsCALCULATOR Bearing stress formula Bearing stress is the contact pressure between a fastener and the hole […]Bending Stress FormulaHome » Formulas & EquationsCALCULATOR Bending stress formula When a beam bends, one face stretches and the other compresses, creating […]Bernoulli Equation FormulaHome » Formulas & EquationsCALCULATOR Bernoulli equation The Bernoulli equation is energy conservation for a flowing fluid. Along a streamline […]Convection Heat Transfer FormulaHome » Formulas & EquationsCALCULATOR Convection heat transfer formula Newton law of cooling gives the heat carried away from a […]Factor of Safety FormulaHome » Formulas & EquationsCALCULATOR Factor of safety formula The factor of safety is how much stronger a part is […]Flow Rate FormulaHome » Formulas & EquationsCALCULATOR Flow rate formula Volumetric flow rate is how much fluid passes a point each second, […]Force FormulaHome » Formulas & EquationsCALCULATOR Force formula (Newton's second law) Newton's second law gives the force needed to accelerate a […]Heat Transfer FormulaHome » Formulas & EquationsCALCULATOR Heat transfer formula This is the sensible-heat equation: the energy needed to change the temperature […]Horsepower FormulaHome » Formulas & EquationsCALCULATOR Horsepower formula Horsepower measures the rate of doing work. For a rotating shaft it comes […]Kinetic Energy FormulaHome » Formulas & EquationsCALCULATOR Kinetic energy formula Kinetic energy is the energy an object has because of its motion. […]Moment FormulaHome » Formulas & EquationsCALCULATOR Moment formula A moment is the turning effect of a force about a point, equal […]Polar Moment of Inertia FormulaHome » Formulas & EquationsCALCULATOR Polar moment of inertia formula The polar moment of inertia measures how well a round […]Pressure Drop FormulaHome » Formulas & EquationsCALCULATOR Pressure drop formula The Darcy-Weisbach equation gives the pressure lost to friction as fluid flows […]Pump Horsepower FormulaHome » Formulas & EquationsCALCULATOR Pump horsepower formula Pump horsepower is the power needed to move a liquid at a […]Radiation Heat Transfer FormulaHome » Formulas & EquationsCALCULATOR Radiation heat transfer formula The Stefan-Boltzmann law gives the heat radiated by a surface. It […]Section Modulus FormulaHome » Formulas & EquationsCALCULATOR Section modulus formula Section modulus is the single number that tells you how strong a […]Shear Stress FormulaHome » Formulas & EquationsCALCULATOR Shear stress formula Shear stress is the force acting parallel to a surface divided by […]Strain FormulaHome » Formulas & EquationsCALCULATOR Strain formula Strain measures how much a material stretches or compresses relative to its original […]Stress FormulaHome » Formulas & EquationsCALCULATOR Stress formula Stress is the internal force a material carries spread over its cross-sectional area. […]Thermal Conduction FormulaHome » Formulas & EquationsCALCULATOR Thermal conduction formula Fourier law of conduction gives the rate heat flows through a solid. […]Thermal Expansion FormulaHome » Formulas & EquationsCALCULATOR Thermal expansion formula Most materials grow when heated. The linear thermal expansion formula gives that […]Torque FormulaHome » Formulas & EquationsCALCULATOR Torque formula Torque is the twisting effort produced by a force acting at a distance […]Torque to Horsepower FormulaHome » Formulas & EquationsCALCULATOR Torque to horsepower formula This converts between rotational torque and power in either unit system. […]
📐 Machining 10
Chip Load FormulaChip load is the thickness each flute removes per revolution. Rearrange the feed rate formula to check whether your program […]Cutting Force FormulaThe tangential cutting force is what the spindle pushes against and what tries to deflect the tool. It follows directly […]Cycle Time FormulaThe cutting time for a single straight pass is just the length of the cut divided by the feed rate. […]Feed Rate FormulaFeed rate is how fast the table moves, in inches per minute. It is built from the chip each tooth […]Material Removal Rate FormulaMaterial removal rate (MRR) is the volume of metal cut per minute. It measures how productive a cut is and […]RPM FormulaSpindle RPM is set by the cutting speed your material and tool want (in surface feet per minute) and the […]Spindle Horsepower FormulaSpindle horsepower needed for a cut is the material removal rate multiplied by the unit power (specific cutting energy) of […]Surface Speed FormulaSurface speed (SFM) is how fast the cutting edge travels past the work. Solve it from a known RPM and […]Thread Milling FormulaWhen thread milling, the cutting edge follows a larger circle than the tool center. To get the right feed at […]Tool Deflection FormulaAn end mill bends like a cantilever beam fixed in the holder. The deflection formula shows why stickout and diameter […]
📐 Geometry 8
Area of a Circle FormulaHome » Formulas & EquationsCALCULATOR Area of a circle formula The area of a circle depends only on its radius. […]Circumference FormulaHome » Formulas & EquationsCALCULATOR Circumference formula The circumference is the distance around a circle. It equals pi times the […]Distance FormulaHome » Formulas & EquationsCALCULATOR Distance formula The distance formula gives the straight-line distance between two points on a coordinate […]Law of Cosines FormulaHome » Formulas & EquationsCALCULATOR Law of cosines formula The law of cosines finds a missing side or angle in […]Midpoint FormulaHome » Formulas & EquationsCALCULATOR Midpoint formula The midpoint formula finds the exact point halfway between two points on a […]Pythagorean Theorem FormulaHome » Formulas & EquationsCALCULATOR Pythagorean theorem formula The Pythagorean theorem relates the three sides of a right triangle. The […]Slope FormulaHome » Formulas & EquationsCALCULATOR Slope formula The slope formula measures how steep a line is. It is the change […]Triangle Area FormulaHome » Formulas & EquationsCALCULATOR Area of a triangle formula The most common way to find a triangle's area is […]
📐 Auto 8
Battery Runtime FormulaBattery runtime estimates how long a battery powers a load from its amp-hour capacity. Runtime (h) = Capacity (Ah) ÷ […]Brake Distance FormulaBraking distance is how far a vehicle travels while decelerating to a stop, set by speed and tire grip. Braking […]Compression Ratio FormulaCompression ratio compares the cylinder volume at the bottom of the stroke to the volume at the top — how […]Engine Displacement FormulaDisplacement is the total volume the pistons sweep — the headline size of an engine. Displacement = (π ÷ 4) […]Fuel Economy FormulaFuel economy is simply how far you go on a unit of fuel. MPG = Distance ÷ Fuel Used Where […]Gear Ratio FormulaA gear ratio compares the input and output of a gear set, showing how it trades speed for torque. Gear […]Power to Weight FormulaPower-to-weight ratio is the best single predictor of acceleration — it normalizes engine output against how much mass it has […]Speed FormulaSpeed is the rate of covering distance — the most basic relationship in motion. Speed = Distance ÷ Time Where […]
📐 Statistics 5
Combination FormulaHome » Formulas & EquationsCALCULATOR Combination formula A combination counts the ways to choose r items from n when order […]Permutation FormulaHome » Formulas & EquationsCALCULATOR Permutation formula A permutation counts the ways to arrange r items chosen from n when […]Probability FormulaHome » Formulas & EquationsCALCULATOR Probability formula The basic probability formula gives the chance of an event as the number […]Standard Deviation FormulaHome » Formulas & EquationsCALCULATOR Standard deviation formula Standard deviation measures how spread out a data set is around its […]Z Score FormulaHome » Formulas & EquationsCALCULATOR Z score formula A z-score tells you how many standard deviations a value lies from […]
📐 Recipe & Servings 4
Food Cost FormulaFood cost tells you what the ingredients in a dish cost, and as a percentage of price, whether it is […]Recipe Scaling FormulaScaling a recipe up or down comes down to one multiplier applied to every ingredient. Scaling factor = Desired servings […]Serving Size FormulaServing size is just the total amount a recipe makes divided evenly across the number of portions. Serving size = […]Yield FormulaYield percentage captures how much usable food remains after trimming, peeling, or cooking loss — essential for buying the right […]
📐 Algebra 3
Compound Interest FormulaHome » Formulas & EquationsCALCULATOR Compound interest formula Compound interest grows money faster than simple interest because each period earns […]Linear Equation FormulaHome » Formulas & EquationsCALCULATOR Linear equation formula A linear equation describes a straight line. The slope-intercept form, y equals […]Quadratic FormulaHome » Formulas & EquationsCALCULATOR Quadratic formula The quadratic formula solves any equation of the form a x squared plus […]
⚡ Electrical 3
Ohms Law FormulaHome » Formulas & EquationsCALCULATOR Ohm's law formula Ohm's law links the voltage across a component to the current through […]RC Time Constant FormulaHome » Formulas & EquationsCALCULATOR RC time constant formula The RC time constant sets how fast a capacitor charges or […]Three-Phase Power FormulaHome » Formulas & EquationsCALCULATOR Three-phase power formula Three-phase power is the standard for industrial and commercial electrical systems. This […]
🧁 Baking 2
📐 Nutrition & Health 2
What you will find here
Every page covers one formula: the equation itself, a plain-English definition of each term, the rearranged forms for solving for any unknown, a fully worked numeric example, and the correct units. We add formulas as the calculator library grows, spanning physics, math, engineering, electrical, and everyday calculations.
How to use a formula page
Start with the equation and the variable definitions to understand what the formula needs. If you are solving for something other than the usual output, use the rearranged forms. Follow the worked example with your own numbers, and when you want the answer checked instantly, click through to the matching calculator.
Formulas vs calculators
A formula page teaches you how the math works and lets you compute by hand; a calculator does it for you in one step. They are meant to be used together — learn the formula here, then reach for the calculator when you just need the result.
Formulas FAQ
Are these formula pages free?
Yes. Every formula page is free to read, use on mobile, and print, with no sign-up.
Do the pages show how to rearrange the formula?
Yes. Each page lists the rearranged forms so you can solve for any variable, not just the usual output.
What units should I use?
Each page states the standard units for every variable. Keeping consistent units is the most common source of formula errors, so we call them out explicitly.
Can I check my answer?
Every formula page links to the matching calculator, so you can run your numbers and confirm the result instantly.
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