Throughout my career as a product designer and inventor, I've encountered the same challenge countless times: how do you take a standard DC motor—spinning at 10,000's of rpm with less than 0.5 Nm of torque—and transform it into something useful that can actually move a load, lift a weight, or drive a mechanism?
GO TO GEAR DESIGN TOOL
The answer is always gears. Whether I'ts an actuator, a powered hand tool, or an automated mechanism, you need to convert high-speed, low-torque motor output into low-speed, high-torque mechanical power. Every single project involves this fundamental trade-off.
A good tip is to repurpose power tools when you need to validate an idea quickly.
I’ve made countless proof-of-concept prototypes using cordless drill gearboxes, motors, and batteries—something that comes naturally from my time at Stanley Black & Decker (DeWalt). Power tools are exceptionally well designed, making them an easy way to get usable torque fast for quick-and-dirty prototypes. Many power tools use planetary gearboxes, which I’m particularly fond of, as they deliver high gear ratios in a compact, multi-stage package
I created this gear calculator primarily for myself because I got tired of the tedious, repetitive calculations required at the concept stage of every project. This isn't a full gear design suite—it won't generate manufacturing drawings or perform finite element analysis.
It will give you a preview of the gears in each stage too and you can download a report for later reference.
But it does exactly what I need when I'm sitting at my desk sketching ideas: it tells me quickly whether my concept is feasible.
Can I get a 50:1 reduction in a 100mm package? Will standard off-the-shelf gears work, or do I need custom gears that'll blow my budget? What module do I need to handle 5 Nm of torque without breaking teeth? These are the questions you need answered in the first hour of design, not after you've committed to a direction.
The tool includes a switch to specify standard catalog gears because that's how real products get designed economically. At the concept stage, you're not trying to optimize every millimeter—you're trying to determine what's actually buildable and affordable. Can I source these gears from HPC, Boston Gear or SDP/SI and have them next week?
Or am I looking at custom gear cutting, 8-week lead times, and tooling costs that kill the project before it starts? This calculator helps you make those early decisions quickly, so you can iterate through concepts rapidly and land on a design direction that's both functional and practical.
It won’t delve into the complexities and subtleties of addendum modification, for example, as gear design is highly specialised and complex. However, I hope this tool will be useful at the very start of a design, helping you lay out and allocate space with far more confidence than simply relying on a rough estimate.
In my experience, I’ve never worked on a product where the brief was anything like, “Take as much space as you like — the bigger, the better.” It’s almost always, “The smaller, the better… and can you shave off a few millimetres, please?
Once you've validated the concept here, then you move to detailed CAD, supplier quotes, and proper engineering analysis. But this gets you 80% of the way there in a fraction of the time.
Professional gear calculator for mechanical engineers and product designers. Calculate precise gear dimensions, ratios, and performance for spur gears, helical gears, bevel gears, and planetary (epicyclic) gearboxes. Supports metric module (DIN 780, ISO standards) and imperial diametral pitch (AGMA standards) with multi-stage gearbox calculations up to 4 stages. Includes contact ratio analysis, AGMA bending stress calculations, Hertzian contact stress analysis, and material selection for steel, aluminum, bronze, cast iron, and engineered plastics.
Gears are the fundamental building blocks of mechanical power transmission. Every machine that converts rotational speed and torque—from watches to wind turbines—relies on precisely designed gears. Proper gear design requires accurate calculation of tooth dimensions, gear ratios, center distances, contact ratios, and strength verification. Incorrect gear design leads to noise, vibration, premature wear, catastrophic tooth failure, or inability to transmit required power. This calculator provides engineering-grade calculations based on international standards to ensure your gears will mesh properly and perform reliably.
The fundamental relationship in gear design: Speed reduction equals torque multiplication. A 3:1 gear ratio reduces output speed to one-third of input speed while (theoretically) tripling output torque. Understanding this relationship is critical for sizing motors, selecting gear ratios, and designing gearboxes that meet your application requirements for speed, torque, and power transmission.
The gear world is divided into two incompatible standards for defining tooth size: Module (metric) and Diametral Pitch (imperial). These systems are NOT interchangeable—you cannot mesh a metric gear with an imperial gear under any circumstances.
Module (m) is the metric standard used worldwide, particularly in Europe and Asia. Module equals pitch diameter (mm) divided by number of teeth: m = d/z. Larger module numbers mean larger, stronger teeth. Module 1.0mm produces small, fine teeth suitable for instruments. Module 5.0mm produces large, robust teeth for industrial machinery. Standard module values follow the DIN 780 series: 0.5, 0.75, 1.0, 1.25, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0, 6.0, 8.0, 10.0, 12.0, 16.0, 20.0mm. Always select standard module values—custom modules require special tooling and dramatically increase cost.
Diametral Pitch (DP) is the imperial standard used primarily in North America. DP equals number of teeth divided by pitch diameter (inches): DP = z/d. Larger DP numbers mean smaller, finer teeth (opposite of module). DP 12 produces moderately-sized teeth common in general machinery. DP 48 produces tiny teeth for instruments. Standard DP values per AGMA: 48, 32, 24, 20, 16, 12, 10, 8, 6, 5, 4, 3, 2.5, 2, 1.5, 1. Like module, always use standard values to avoid custom tooling costs.
Quick conversion between systems (approximate): Module (mm) ≈ 25.4 / Diametral Pitch. Module 2.0mm ≈ DP 12.7. However, you should never actually convert between systems—always design in one system from the start and source all gears to that same standard.
Spur gears have straight teeth parallel to the gear axis. They're the simplest, most common, and most efficient gear type for parallel shaft power transmission. Key characteristics:
Spur gear design considerations: Minimum teeth to avoid undercutting: 17 teeth for 20° pressure angle, 32 teeth for 14.5° pressure angle, 12 teeth for 25° pressure angle. Contact ratio should be minimum 1.2, preferably 1.4+ for smooth operation. Face width typically 3-5× module for balanced strength and manufacturing economy. Use hardened steel gears for high loads or high-speed applications requiring long life.
Helical gears have teeth cut at an angle (helix angle) to the gear axis. The angled teeth engage gradually rather than suddenly, providing smooth, quiet operation. Helical gears are the preferred choice for automotive transmissions, high-speed machinery, and applications where noise reduction is critical. Key characteristics:
Helical gear design considerations: Right-hand and left-hand helices must match correctly for meshing pairs. Opposite hand helices for external gears on parallel shafts. Same hand for crossed helical gears (non-parallel shafts). Helix angle increases contact ratio significantly—helical gears naturally have higher contact ratios than spur gears of same size. Face width typically 4-6× module to fully utilize helix benefits. Always specify helix angle and hand on drawings.
Bevel gears transmit power between intersecting shafts, most commonly at 90° angles. Teeth are cut on cone-shaped surfaces rather than cylinders. Common in automotive differentials, right-angle gearboxes, and machine tools requiring right-angle drives. Two main types:
Bevel gear design considerations: Mounting is critical—bevel gears are very sensitive to misalignment. Requires precise bearings and rigid housings. Pitch angle depends on gear ratio—equal 45° angles for 1:1 ratio, unequal for other ratios. Face width typically limited to 1/3 of cone distance for proper tooth geometry. Always mount bevel gears in matched pairs—individual gears aren't interchangeable. Common shaft angles: 90° (most common), 60°, 120°, or custom angles as required by application.
Planetary (epicyclic) gear systems provide high gear ratios in extremely compact packages with unique configuration: Sun gear (center input), Planet gears (typically 3-4 gears orbiting sun), Ring gear (outer gear with internal teeth), Carrier (holds planets and provides output). This configuration enables coaxial input and output shafts with multiple load paths for high torque capacity.
Key advantages of planetary gears:
Planetary gear design rules: The teeth must satisfy geometric constraint: Ring Teeth = Sun Teeth + 2 × Planet Teeth. This ensures proper center distances. Number of planets typically 3 or 4. More planets = higher load capacity but increased complexity and cost. Planets must be equally spaced around sun: 120° spacing for 3 planets, 90° spacing for 4 planets. (Sun Teeth + Ring Teeth) must be evenly divisible by number of planets for equal load sharing. Typical ratios: 3:1 to 10:1 per stage. Higher single-stage ratios possible but require very large ring/planet size difference.
Common planetary gear applications: Automatic transmissions (automotive), Electric screwdriver and drill reduction gearboxes, Wind turbine main gearboxes, Industrial servo systems, Aerospace actuators, Robotics joint drives, Heavy equipment final drives, Machine tool spindle drives. Use planetary when you need: high ratio in minimum space, high torque capacity, coaxial input/output, or multiple load paths for reliability.
Single-stage gear pairs are limited to practical ratios around 6:1 to 10:1. Higher single-stage ratios create very large size differences between pinion and gear, leading to problematic issues: very small pinion with too few teeth (undercutting risk), very large gear with excessive inertia and size, poor load distribution across unequal tooth engagement, limited contact ratio causing noise and wear.
Multi-stage gearboxes solve this by using multiple gear pairs in series. Output of first stage becomes input to second stage. Output of second stage becomes input to third stage, etc. Total ratio equals product of all individual stage ratios: Total Ratio = Stage1 × Stage2 × Stage3 × Stage4.
Multi-stage benefits: Achieve very high ratios (100:1, 500:1, even 10,000:1) using reasonable gear sizes throughout. Each stage uses moderate ratio (3:1 to 6:1) with practical gear sizes. Distribute loads across multiple gear sets reducing stress on any single gear. More compact than equivalent single-stage (which would require enormous gear size). Flexibility to mix gear types: spur + helical, helical + planetary, etc., optimizing each stage for its specific requirements.
Multi-stage design example: Need 50:1 reduction from 1500 RPM motor to 30 RPM output. Single stage would require 15 teeth / 750 teeth (impractical—huge gear, tiny pinion). Three-stage design: Stage 1: 20T/70T = 3.5:1, Stage 2: 18T/65T = 3.61:1, Stage 3: 20T/78T = 3.9:1. Total: 3.5 × 3.61 × 3.9 = 49.2:1 (close enough). All gears are reasonable sizes: 18-78 teeth range. Output: 1500 RPM / 49.2 = 30.5 RPM. Output torque: Input × 49.2 (assuming 100% efficiency, actual ~95% accounting for friction losses).
Pressure angle is the angle between tooth force direction and tangent to pitch circle. It fundamentally affects tooth strength, sliding friction, and efficiency. Three standard pressure angles are used:
Important pressure angle rule: Both gears in meshing pair MUST have identical pressure angle. You cannot mesh a 20° gear with a 25° gear—teeth won't engage properly and will rapidly destroy each other. This is a hard constraint with no exceptions. When specifying gears, always clearly state pressure angle on drawings and purchase orders.
Contact ratio indicates the average number of teeth in contact during gear rotation. If contact ratio = 1.5, on average 1.5 teeth are engaged at any moment. Higher contact ratios provide multiple benefits: smoother operation (less vibration), quieter operation (gradual load transfer between teeth), higher load capacity (load shared across more teeth), extended gear life (lower stress per tooth).
Contact ratio guidelines:
How to increase contact ratio: Increase number of teeth on both gears (larger gears), Use longer tooth addendum (profile shift modification), Switch from spur to helical gears (helix angle dramatically increases contact ratio), Decrease pressure angle (but this weakens teeth—usually not recommended), Increase face width (doesn't directly increase contact ratio but improves load distribution).
Gear material selection depends on required strength, wear resistance, noise characteristics, operating environment, and cost constraints. This calculator includes AGMA bending stress and Hertzian contact stress calculations for common gear materials:
Steel Gears: Most common material for power transmission. Through-hardened steel (typical: 1045, 4140, 4340 steels heat treated to 250-300 HB): Good strength, moderate cost, used for general machinery. Case-hardened steel (typical: 8620, 9310 carburized and hardened to 58-62 HRC surface): Excellent wear resistance with tough core. Standard for automotive transmissions and high-load applications. Induction-hardened steel: Surface hardening without carburizing. Faster process for larger gears. Allowable bending stress: 200-400 MPa depending on hardness and quality. Allowable contact stress: 800-1500 MPa for hardened gears.
Cast Iron Gears: Gray cast iron or ductile iron. Lower strength than steel but excellent damping properties (quieter operation), good machinability, lower cost for large gears, self-lubricating properties. Used for large, low-speed gears in machine tools, elevators, mixers. Allowable bending stress: 50-100 MPa. Allowable contact stress: 400-700 MPa. Not suitable for high speeds or shock loads.
Bronze Gears: Typically phosphor bronze or aluminum bronze. Used when one gear must be softer than mate to prevent damage to more expensive gear, excellent corrosion resistance for marine applications, non-sparking for hazardous environments, quiet operation with low friction. Standard practice: bronze gear paired with hardened steel pinion. Bronze sacrificial wear protects steel pinion. Used in worm gearboxes, marine drives, food processing equipment. Allowable bending stress: 40-80 MPa. Allowable contact stress: 300-500 MPa.
Aluminum Gears: Lightweight (1/3 weight of steel), good for low-load, high-speed applications where inertia matters, easy to machine (rapid prototyping), excellent corrosion resistance, relatively low cost. Used in aerospace (weight-critical), robotics, instruments, drones. Allowable bending stress: 30-60 MPa. Allowable contact stress: 200-400 MPa depending on alloy.
Plastic Gears: Injection molded nylon, acetal (Delrin), PEEK, or other engineering plastics. Very quiet operation (plastic naturally dampens noise), no lubrication required (self-lubricating), corrosion-proof, lightweight, low cost for high-volume production. Used in consumer products, printers, automotive interior mechanisms, toys, medical devices. Limitations: Low load capacity (10-20% of steel), temperature sensitive (most limited to 80-120°C), wear more rapidly than metal, higher thermal expansion (requires looser backlash). Allowable bending stress: 15-40 MPa. Allowable contact stress: 50-150 MPa.
Gear teeth act as cantilever beams subjected to bending loads. AGMA 2001 standard provides methodology for calculating bending stress at tooth root—the highest stress location where tooth breakage initiates. Lewis equation (modified by AGMA): Bending Stress = (Tangential Force) / (Face Width × Module × Y-factor) where Y-factor is Lewis form factor depending on tooth count and pressure angle.
Calculated bending stress must be less than material's allowable bending stress with appropriate safety factor. Safety factor guidelines: 1.5-2.0 for steady loads, known materials, controlled environment. 2.5-3.0 for variable loads, uncertain materials, harsh environment. 3.5+ for shock loads, critical applications, safety-critical components.
If bending stress exceeds allowable: Increase module (larger, stronger teeth), Select stronger material (steel instead of aluminum, hardened instead of unhardened), Increase face width (distributes load over longer teeth), Reduce input torque or use multi-stage gearbox to divide loads, Add more gear stages to reduce torque per stage, Use higher quality material with better allowable stress.
Gear tooth surfaces experience high contact pressure where teeth mesh. Hertzian contact theory calculates this pressure based on gear geometry, materials, and loads. Excessive contact stress causes surface pitting—small craters form on tooth surfaces due to fatigue, surface spalling and flaking, progressive surface deterioration, eventual complete tooth surface destruction.
Hertzian contact stress = f(Tangential Force, Geometry, Material Properties). Higher for smaller gears, higher loads, softer materials. Calculated contact stress must be less than material's allowable contact stress with appropriate safety factor. Hardened steel gears can handle 1000-1500 MPa contact stress. Unhardened steel limited to 600-800 MPa. Plastics limited to 50-150 MPa depending on material grade.
If contact stress exceeds allowable: Use hardened steel gears instead of unhardened, Increase module to increase tooth surface area, Increase face width to spread load, Use crowned teeth to prevent edge loading, Improve surface finish (smoother surfaces resist pitting), Ensure proper lubrication (oil film separates surfaces), Reduce operating loads or add more stages to divide loads.
Stock gears are available from multiple suppliers in standard sizes, dramatically reducing cost and lead time compared to custom gears. Standard gear catalogs typically offer: Module 0.5 to 10.0mm (metric), DP 48 to 4 (imperial), 12 to 120 teeth in 1-2 tooth increments, 20° pressure angle standard (14.5° and 25° limited availability), Steel, brass, and plastic materials, Various bore sizes and keyway options.
Benefits of using standard catalog gears: Available immediately (no manufacturing lead time), Much lower cost than custom-cut gears, Proven quality from reputable manufacturers, Easy replacement—order another identical gear when needed, Documented specifications and load ratings. Design strategy: Whenever possible, design gearbox around available standard gears rather than specifying custom gears. Use this calculator to determine required gear specifications, then search standard catalogs (Boston Gear, Martin, SDP/SI, Misumi, KHK) to find closest matches.
This professional gear calculator is completely free with no restrictions, no premium features, no required login, and no data collection. Designed to help mechanical engineers, product designers, students, inventors, and manufacturing professionals quickly design and analyze gear systems based on international standards (DIN 780, ISO, AGMA 2001). The tool runs entirely in your browser—no calculations or sensitive design data are transmitted to external servers. All your gear specifications remain private.
Use this calculator for preliminary design, concept evaluation, design validation, student homework and learning, professional engineering work, manufacturing quotes, gear replacement specifications, and failure analysis investigations. Copy results into your CAD software, engineering reports, manufacturing drawings, and technical documentation. Export to PDF for design records, or export DXF files for direct CAD import of tooth profiles.
Gear design is fundamental mechanical engineering combining geometry, strength of materials, tribology, manufacturing, and practical experience. This free tool makes professional-grade gear calculations accessible to everyone committed to designing reliable, efficient power transmission systems.
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