- Estimated bending safety factor is below 1.00.
- Estimated contact safety factor is below 1.00.
- Contact ratio is favorable for smooth tooth engagement.
| Property | Pinion | Gear | Unit |
|---|---|---|---|
| Tooth count | 20 | 60 | teeth |
| Pitch diameter | 50.000 | 150.000 | mm |
| Outside diameter | 55.000 | 155.000 | mm |
| Root diameter | 43.750 | 143.750 | mm |
| Base diameter | 46.985 | 140.954 | mm |
| Rotational speed | 1,450.000 | 483.333 | rpm |
| Torque | 49.397 | 143.744 | N·m |
| Bending safety | 0.520 | 0.472 | ratio |
| Contact safety | 1.222 | 0.838 | ratio |
| Mass estimate | 0.444 | 3.607 | kg |
Design snapshot
Reverse result
Pitch diameter divided by tooth count.
| Geometry item | Value | Unit | Meaning |
|---|---|---|---|
| Module | 2.500 | mm | Pitch diameter per tooth. |
| Diametral pitch | 10.160 | teeth/in | Teeth per inch of pitch diameter. |
| Circular pitch | 7.854 | mm | Arc distance between corresponding teeth. |
| Base pitch | 7.380 | mm | Tooth spacing along the base circle. |
| Tooth thickness | 3.887 | mm | Approximate pitch-circle thickness. |
| Tooth-space width | 3.967 | mm | Pitch-circle space after backlash. |
| Whole depth | 5.625 | mm | Addendum plus dedendum. |
| Working depth | 5.000 | mm | Depth shared by mating teeth. |
| Clearance | 0.625 | mm | Root-to-tip radial clearance. |
| Standard center distance | 100.000 | mm | Unshifted reference center distance. |
| Profile-adjusted center | 100.000 | mm | Approximate center after total shift. |
| Working pressure angle | 20.000 | deg | Operating line-of-action angle. |
| Path of approach | 6.586 | mm | Contact before pitch point. |
| Path of recess | 5.745 | mm | Contact after pitch point. |
| Total path of contact | 12.331 | mm | Usable line-of-action contact length. |
| Arc of contact | 13.122 | mm | Pitch-circle contact arc. |
| Minimum undercut-free teeth | 18 | teeth | Approximate zero-shift limit. |
| Performance item | Value | Unit | Formula basis |
|---|---|---|---|
| Input power | 7.500 | kW | Entered or derived from torque. |
| Output power | 7.275 | kW | Input power multiplied by efficiency. |
| Power loss | 0.225 | kW | Input minus output power. |
| Input torque | 49.397 | N·m | 9550P/N. |
| Output torque | 143.744 | N·m | Input torque × ratio × efficiency. |
| Pitch-line velocity | 3.796 | m/s | πdN/60. |
| Tangential tooth force | 1,975.862 | N | 2T/d. |
| Radial separating force | 719.155 | N | Ft tan φw. |
| Normal tooth force | 2,102.668 | N | Ft/cos φw. |
| Resultant tooth force | 2,102.668 | N | Vector resultant. |
| Axial force | 0 | N | Zero for ideal spur gears. |
| Approximate reaction per bearing | 1,051.334 | N | Equal two-bearing load split. |
| Pinion load cycles | 1.740e+9 | cycles | RPM × 60 × life hours. |
| Gear load cycles | 5.800e+8 | cycles | RPM × 60 × life hours. |
| Strength item | Pinion | Gear | Unit |
|---|---|---|---|
| Material | Alloy steel, through hardened | Carbon steel, normalized | preset |
| Allowable bending stress | 240.000 | 170.000 | MPa |
| Lewis form factor | 0.108 | 0.139 | ratio |
| Estimated bending stress | 461.156 | 360.154 | MPa |
| Bending safety factor | 0.520 | 0.472 | ratio |
| Allowable contact stress | 1,050.000 | 720.000 | MPa |
| Estimated contact stress | 859.512 | MPa | |
| Contact safety factor | 1.222 | 0.838 | ratio |
| Combined load factor | 1.581 | ratio | |
| Required face width, bending | 52.964 | mm | |
| Required face width, contact | 35.627 | mm | |
| Controlling face-width estimate | 52.964 | mm | |
| Preliminary maximum torque | 23.316 | N·m | |
| Preliminary maximum power | 3.540 | kW | |
| Manufacturing item | Pinion | Gear | Unit |
|---|---|---|---|
| Chordal tooth thickness | 3.883 | 3.887 | mm |
| Chordal addendum | 2.576 | 2.525 | mm |
| Base tangent length | 19.151 | 50.073 | mm |
| Approximate measurement over pins | 49.302 | 149.302 | mm |
| Pin or ball diameter | 4.000 | mm | |
| Blank outside diameter | 55.300 | 155.300 | mm |
| Suggested fillet radius | 0.875 | mm | |
| Estimated pitch error | 0.010 | mm | |
| Estimated radial runout | 0.019 | mm | |
| Polar inertia estimate | 0.000 | 0.011 | kg·m² |
Pin measurements are approximate. Validate exact involute inspection values with the selected standard, profile shift, pin size, and tooth-thickness specification.
Pitch diameter divided by tooth count.
Diagram legend
Spur gear calculator inputs
Choose a tooth system, enter gear geometry, specify operating loads, and select materials. Submit for complete server results.
This preview updates before submission.
Formula used
Reference geometry
da = d + 2m(ha* + x)
df = d - 2m(hf* - x)
db = d cos φ
p = πm
pb = πm cos φ
Ratio, speed, and torque
N₂ = N₁ / i
T₁ = 9550P / N₁
T₂ = T₁ × i × η
v = πd₁N₁ / 60
Tooth forces
Fr = Ft tan φw
Fn = Ft / cos φw
Fa = 0
Preliminary bending
Sb = σallow / σb
Y ≈ 0.154 - 0.912/z
Preliminary contact stress
SH = σH,allow / σH
I ≈ cosφ sinφ · i / [2(i+1)]
Contact ratio
How to use this calculator
- Select module or diametral pitch input.
- Choose a standard tooth system or custom proportions.
- Enter pinion and gear tooth counts.
- Provide face width, bores, hubs, and backlash.
- Choose power or torque as the driving input.
- Enter speed, efficiency, and load factors.
- Select materials or enter custom material properties.
- Review geometry, force, contact, and strength results.
- Resolve warnings before using any preliminary design.
- Export the report for documentation and review.
Example data table
| Example | Module | Pinion teeth | Gear teeth | Speed | Power | Use case |
|---|---|---|---|---|---|---|
| Small reducer | 1.5 mm | 18 | 54 | 1800 rpm | 1.1 kW | Compact machinery |
| General industrial | 2.5 mm | 20 | 60 | 1450 rpm | 7.5 kW | Three-to-one reduction |
| High torque | 5 mm | 24 | 72 | 960 rpm | 30 kW | Heavy conveyor |
| Imperial concept | 12 DP | 24 | 48 | 1750 rpm | 5 hp equivalent | Two-to-one reduction |
| Plastic quiet drive | 1 mm | 25 | 75 | 600 rpm | 0.15 kW | Light-duty device |
Spur gear design guide
What a spur gear does
Spur gears transfer rotary motion between parallel shafts. Their teeth run straight across each face. This geometry makes production practical. It also makes inspection straightforward. A matched pair changes speed and torque. The tooth-count ratio controls that change. External gears rotate in opposite directions. An idler can change direction without changing ratio.
Module and diametral pitch
Module describes tooth size in metric systems. It equals pitch diameter divided by teeth. Larger modules produce larger teeth. Diametral pitch serves a similar imperial purpose. It equals teeth divided by pitch diameter in inches. Module and diametral pitch are reciprocal after unit conversion. Mating gears must use compatible tooth size.
Pressure angle and tooth geometry
The pressure angle defines the line of action. Twenty degrees is widely used. Smaller angles can reduce radial force. They may also increase undercut risk. Larger angles strengthen roots. They also increase bearing separation forces. Addendum extends above the pitch circle. Dedendum extends below it. Clearance prevents tip and root interference.
Ratio, speed, and torque
The driven gear ratio equals driven teeth divided by pinion teeth. Output speed falls as ratio rises. Ideal torque rises by the same ratio. Real output torque also depends on efficiency. Power losses become heat. Lubrication and alignment influence those losses. Shaft, key, and bearing capacity remain separate checks.
Contact ratio and undercut
Contact ratio estimates average tooth engagement. Values above one preserve continuous contact. Higher values often improve smoothness. Very low values raise noise sensitivity. Small pinions can develop undercut. Positive profile shift can help. It also changes outside diameter and working geometry. Modified designs need careful inspection.
Strength and durability
Tooth roots experience bending stress. Tooth flanks experience contact stress. Surface fatigue can produce pitting. Root fatigue can produce cracks. Face width spreads load. Material hardness changes allowable stress. Dynamic loads increase with speed and error. Service factors represent shock, alignment, reliability, and temperature.
Manufacturing and verification
Manufacturing drawings need more than pitch diameter. They may specify blank size, bore, hub, keyway, runout, tooth thickness, span measurement, and measurement over pins. Heat treatment can change final dimensions. Inspection methods depend on the selected standard. Exact tolerances should match machine capability. Professional engineering review remains essential for safety-critical gear assemblies.
Frequently asked questions
What module should I choose?
Choose a standard module that satisfies strength, size, and manufacturing needs. Start with torque and face width. Then verify root stress, contact stress, center distance, and available cutters.
Can gears with different modules mesh?
No. Standard spur gears must share the same module or equivalent diametral pitch. They should also share pressure angle and compatible tooth proportions.
Why is the axial force zero?
An ideal spur gear has zero helix angle. Therefore, it creates tangential and radial forces without a theoretical axial component. Misalignment can still create unintended thrust.
What is a good contact ratio?
A value above one is essential for continuous contact. Values around 1.4 or higher often provide smoother engagement. Exact targets depend on speed, noise, and manufacturing quality.
Does this calculator replace AGMA or ISO rating?
No. Its strength estimates are simplified screening calculations. Formal rating requires detailed standard factors, material data, reliability targets, life factors, lubrication, and validated geometry.
How does profile shift help?
Positive profile shift can strengthen a small pinion root and reduce undercut. It changes tooth thickness, outside diameter, center distance, pressure angle, and contact ratio.
Why does face width matter?
Greater face width lowers average tooth stress. Excessive width can worsen load distribution when shafts or housings deflect. Alignment quality becomes increasingly important.
How accurate is measurement over pins?
The displayed value is an approximate planning result. Exact inspection dimensions require the selected involute standard, tooth thickness, profile shift, pin size, and tolerance method.