Gear Ratio Calculator
The Gear Ratio Calculator computes the mechanical advantage between meshing gears from tooth counts. Determine output RPM, torque multiplication, and overall gear train ratios for single-stage and compound systems.
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What is Gear Ratio?
Gear ratio is the ratio of teeth on the driven gear to teeth on the driving gear. A 60-tooth driven gear meshed with a 20-tooth driving gear creates a 3:1 ratio — the driving gear rotates 3 times for every 1 rotation of the driven gear, tripling torque while reducing speed by one-third.
Gear ratios are fundamental in automotive transmissions, industrial gearboxes, clock mechanisms, bicycle drivetrains, and robotics. Understanding gear ratios allows engineers to match motor speed and torque to application requirements precisely.
使用される計算公式・方程式
この計算ツールは5つの主要な公式を使用しています：
1 Gear Ratio ▼
Driven (60 teeth) / Driver (20 teeth) = 3:1 ratio.
2 Output RPM ▼
Input 3600 RPM with 3:1 ratio: Output = 3600 / 3 = 1200 RPM.
3 Compound Gear Train Ratio ▼
Two stages of 3:1 and 4:1: Overall = 3 × 4 = 12:1 total reduction.
比率計算ツールの使い方
この比率計算ツールは、以下の3ステップで簡単にご利用いただけます：
数値を入力
入力欄に既知の比率の値を入力します。求めたい未知数の入力欄は空欄のままにしておきます。
モードを選択
比率モード（解く、簡素化、スケーリング）を選択します。各モードで異なる計算式が適用されます。
結果を確認
計算するボタンを押します。結果画面に答えと、視覚的な比率バー、円グラフ、詳細なステップバイステップの解決プロセスが表示されます。
実例問題と段階的な解説
本比率計算ツールを使って、以下の3つの例題をステップバイステップで解決するプロセスです：
入力 1 40-tooth gear driven by 10-tooth pinion
入力 2 Motor at 1800 RPM through 5:1 gearbox
入力 3 Two-stage reducer: 3:1 and 4:1
よくある質問 (FAQ)
What does a higher gear ratio mean? ▼
A higher gear ratio (like 5:1 vs 2:1) means more speed reduction and more torque multiplication. The driving gear spins more times per output rotation. This is common in first gear of transmissions for starting from a stop.
How do compound gear trains work? ▼
Compound trains stack multiple gear pairs. Each pair's ratio is multiplied together. Three stages of 3:1 each give 3³ = 27:1 overall ratio. This allows massive speed reductions in a compact package.
What is a gear reduction vs overdrive? ▼
Reduction means the output is slower than input (ratio > 1). Overdrive means output is faster than input (ratio < 1). Cars use overdrive gears (like 0.75:1) for highway fuel economy.
How do I calculate gear ratio for a specific output speed? ▼
Gear Ratio = Input RPM / Desired Output RPM. To get 500 RPM from a 3000 RPM motor: Ratio = 3000/500 = 6:1. Then choose gear teeth: 12T driver / 72T driven = 6:1.
Does gear ratio affect power output? ▼
No. Power (watts) is conserved through the gear train (minus friction losses of 1-5% per stage). A 3:1 ratio multiplies torque by 3× but divides speed by 3×. Power = Torque × Speed remains constant.