Spur Gear Calculator

• •Use the Spur Gear Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
• •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
• •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
• •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
• •Use it in the field when a quick estimate is needed and a full engineering software package is not available.

The Spur Gear Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Lewis bending stress, AGMA contact stress, gear ratio, pitch diameters. Input module or diametral pitch, number of teeth, face width, power, RPM. All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

Spur gears are the simplest type of gear, with teeth cut parallel to the axis of rotation, enabling power transmission between parallel shafts. Key spur gear parameters include: number of teeth (N), module (m) or diametral pitch (P_d), pitch diameter (d = m·N for SI, d = N/P_d for US), pressure angle (typically 20°), face width, and addendum/dedendum. Module (SI) or diametral pitch (US) characterizes tooth size: common modules are 1-10 mm, common diametral pitches are 4-64 per inch. Gear ratio is the ratio of teeth: GR = N_driven/N_driver, and output speed is input speed divided by GR. Center distance between mating gears is C = (d₁ + d₂)/2 = (m·(N₁+N₂))/2. Contact ratio (number of tooth pairs in contact at any time) should be > 1.2 for smooth operation, typically 1.4-1.7 for well-designed gears. Bending strength of gear teeth is computed using the Lewis equation or AGMA methods, considering transmitted load, tooth geometry, and material properties. Surface durability (pitting resistance) is computed using Hertzian contact stress equations. Modern gear design uses AGMA standards for ratings, efficiency, noise, and life prediction. Spur gears are efficient (97-99%) and simple to manufacture but produce axial thrust (zero for spur, unlike helical) and can be noisier than helical gears at high speeds.

• •Industrial gear boxes: spur gears are the standard for low-to-moderate speed gear reducers used in conveyors, mixers, pumps, and similar machinery.
• •Machine tool spindles: precision spur gears provide accurate speed ratios in lathe and milling machine drive trains.
• •Clock and instrument mechanisms: small spur gears drive hands, indicators, and sub-mechanisms in timepieces and measurement instruments.
• •Hand tools and appliances: power drills, kitchen mixers, and many hand tools use spur gears for speed reduction and torque multiplication.
• •Educational models: spur gears are commonly used in teaching gear design because their geometry is straightforward to analyze and manufacture.