Design a planetary (epicyclic) gear train made of a sun gear, planet gears, a ring gear and a carrier. Change the tooth counts and choose which member to hold fixed to see the gear ratio, output speed, rotation direction and torque multiplication update in real time.
Parameters
Sun gear teeth S
Tooth count of the central sun gear
Planet gear teeth P
Tooth count of the planet pinions that mesh with sun and ring
Input speed
rpm
Speed applied to the input member
Configuration (fixed / input / output)
The gear ratio changes with which member is held fixed
Results
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Ring gear teeth (derived)
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Tooth ratio R/S
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Gear ratio (reduction)
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Output speed (rpm)
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Rotation direction
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Torque multiplication (x)
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Planetary gear train — rotation animation
A face-on view of the sun gear, three planet gears, ring gear and carrier. The fixed member is grey, the input is blue and the output is green, each rotating at its correct relative speed and direction.
Gear ratio with the sun held fixed and with the carrier held fixed. Holding a different member (sun, carrier or ring) gives a completely different ratio; the minus sign means the output rotates opposite to the input.
A "planetary gear" is the kind where gears spin around like planets, right? What makes it different from an ordinary gear pair?
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Nice picture. An ordinary gear pair has two shafts, each fixed in a different place. A planetary gear set — also called an epicyclic gear — has three members that all rotate about the SAME centre axis. There is a sun gear in the middle, an internally-toothed ring gear on the outside, planet gears between them that mesh with both the sun and the ring as they go round, and a carrier that links the planet gears together. Those four parts make one set.
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All three members on the same axis — does that actually buy you anything?
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Two things. First, it is compact: because everything is coaxial, the input and output line up on one axis, so you can bolt it straight onto a motor. Second, it is strong in torque: the load is shared by three to five planet gears at once, so it carries far more torque than a single gear pair of the same size. When you change the tooth counts on the left, the ring tooth count R = S + 2P is set automatically — that relation is the condition for everything to mesh.
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When I change the "Configuration" dropdown, the gear ratio jumps around completely. What is going on there?
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That is the most interesting part of a planetary set. It has three "ports" — sun, carrier and ring. You get a completely different gear ratio depending on which one you HOLD STILL, which you DRIVE as input, and which you take the OUTPUT from. Hold the ring and drive the sun, and you get a moderate reduction in the same direction. Hold the carrier and drive the sun, and the ring spins the OPPOSITE way — an instant reverse gear. Hold the sun and drive the ring, and you get yet another reduction.
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Getting several ratios just by changing what you hold still… is that connected to a car's automatic transmission?
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That is exactly the heart of it. A car's automatic transmission uses brakes and clutches to switch which member of the planetary set is held still. No gears have to be jammed in and out of mesh, so it shifts smoothly even while you are driving. A single compact planetary set — or a stack of them — covers multiple forward ratios, neutral and reverse all at once. Wind-turbine step-up gearboxes, robot joints and EV drivetrains all use this same coaxial, high-torque character too.
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When you reduce speed, does the torque go up?
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Yes — it follows from energy conservation. Ignoring friction losses, the output torque is the input torque times the gear ratio. For a ring-fixed ratio of 4.0, the speed is one quarter and the torque is 4x. That is why even a small motor can move heavy loads once you add a planetary reduction drive. The wheel hubs of construction machinery are packed full of these compact planetary reducers.
Frequently Asked Questions
A planetary gear train has three members: the sun gear (S), the planet gears (P) and the ring gear (R). For the gears to mesh, the ring tooth count is fixed by R = S + 2P. The gear ratio depends on which member you hold fixed. Hold the ring with the sun as input and the carrier as output: i = 1 + R/S. Hold the sun with the ring as input and the carrier as output: i = 1 + S/R. Hold the carrier with the sun as input and the ring as output: i = -R/S (the output rotates in reverse).
A planetary set has three ports - sun, carrier and ring - and simply switching which member you hold still with brakes and clutches gives a completely different gear ratio. No gears ever have to slide in and out of mesh, so the transmission can shift smoothly even while the car is moving. A single compact planetary set, or a stack of them, can provide multiple forward ratios, neutral and reverse, which is exactly the heart of a step-ratio automatic transmission.
Ignoring friction losses, the output torque equals the input torque multiplied by the gear ratio. For a ring-fixed gear ratio of 4.0, the output torque is 4x the input and the output speed is one quarter (energy conservation). On top of that, a planetary set shares the load across several planet gears (typically 3-5), so it carries far more torque than a single gear pair of the same size, making it ideal for robot joints, wind-turbine step-up gearboxes and the wheel hubs of heavy machinery.
When you hold the carrier fixed and use the sun as input and the ring as output, the output rotates opposite to the input. In this case the gear ratio is negative (i = -R/S). On the fixed carrier the planet gears act as idler gears, reversing the sun's rotation as they pass it to the ring. This property lets a single planetary set provide a reverse gear.
Real-World Applications
Automotive automatic transmissions: A step-ratio automatic transmission stacks several planetary gear sets and uses brakes and clutches to selectively hold or couple each member, delivering 6 to 10 forward ratios plus neutral and reverse. Because no gears ever physically slide, it can shift smoothly without interrupting torque. The power-split device of a hybrid car also uses a single planetary set to cleverly distribute the speeds of the engine, motor and generator.
Reduction and step-up gearboxes: Planetary reduction drives keep input and output coaxial and pack a large reduction ratio and high torque into a compact package, so they are widely used in industrial robot joints, on the noses of servo motors and in conveying equipment. Conversely, in wind turbines a planetary gearset works as a step-up gearbox, raising the low rotational speed of the blades to the high speed the generator needs.
Wheel reduction in construction and heavy equipment: The wheel hubs of wheel loaders and dump trucks contain a planetary gear set as the final reduction stage. By fixing the ring gear to the vehicle body, using the sun as input and coupling the carrier directly to the wheel, engineers get a large torque multiplication within a limited hub diameter. Because the load is shared among several planet gears, the unit withstands punishing duty.
Power tools, appliances and EV drivetrains: Planetary gears appear in the reduction sections of electric drills and impact drivers, in electric actuators and in electric-vehicle drive units — anywhere high torque is needed in a small package. In EVs it is common to place a planetary reduction drive between a high-speed motor and the wheels, keeping the motor small and light while still delivering enough drive torque.
Common Misconceptions and Pitfalls
A common misconception is believing the ring gear tooth count can be chosen freely. In a planetary set, for the sun, planets and ring to mesh geometrically, the ring tooth count is always bound by R = S + 2P. In real designs you must also satisfy the assembly condition that lets several planet gears be placed at equal intervals — namely that (S + R) is an integer multiple of the number of planets. This tool computes from the meshing condition R = S + 2P; in practical design, check this assembly condition as well.
Next, the misconception that the planet tooth count P directly drives the gear ratio. Expanding the gear ratio 1 + R/S gives 1 + (S + 2P)/S, so P does influence it through R. But the ring-fixed and sun-fixed gear ratios are essentially set by the ratio of the sun teeth S to the ring teeth R, with the planet teeth P acting mainly as an idler that bridges the two. Changing P changes R, so the ratio does shift indirectly, but it is wrong to assume "more planet teeth always means a larger reduction". Choose the tooth combination from both the required gear ratio and the physical gear size (module x teeth).
Finally, the assumption that the frictionless torque multiplication can be used as-is. The torque multiplication |i| in this tool is the ideal, loss-free value. A real planetary set has meshing losses at the gear contacts, bearing losses and oil-churning losses, giving roughly 1 to 3 percent loss per stage. With multiple stages the losses stack up. Note also that a planetary gear used as a step-up gearbox tends to be less efficient than when used for reduction. Estimate the real output torque by multiplying the calculated value by the efficiency (0.97 to 0.99 per stage).
How to Use
Enter sun gear tooth count (typically 30–50 teeth) in the sunNum field
Set planet gear tooth count (usually 20–40 teeth) using planetNum
Input input shaft speed in rpmNum (e.g., 3000 rpm for motor drive)
The simulator automatically calculates ring gear teeth using the constraint: Ring = Sun + 2×Planet
Read the gear ratio, output speed, torque multiplication, and rotation direction from the output labels
Adjust tooth counts to explore different reduction ratios or speed profiles
Worked Example
Configure a compact automotive transmission stage: sun gear 40 teeth, planet gears 30 teeth each. Ring gear = 40 + 2(30) = 100 teeth. Tooth ratio R/S = 2.5. With input speed 3000 rpm and the ring gear held (fixed), gear ratio = 3.5:1 reduction. Output speed at carrier = 3000 ÷ 3.5 = 857 rpm. Torque multiplication = 3.5×, so 400 N·m input yields 1400 N·m at the output shaft. Rotation direction reverses with odd-numbered planetary stages.
Practical Notes
Ring gear tooth count is derived automatically; verify it satisfies Ring ≥ Sun + 2×Planet to avoid interference
Gear ratio = (Ring + Sun) ÷ Sun when ring is stationary; locking the carrier or sun creates alternative ratios useful for multi-speed gearboxes
For high-speed reduction (10:1+), increase planet tooth count relative to sun to minimize package diameter
Torque capacity depends on module (pitch) and material; check face width and bearing loads during detailed design phase
Epicyclic trains reverse output direction relative to input in standard configurations; verify direction matches your drivetrain requirements