Pulley Ratio Calculator
Calculate the speed ratio and mechanical advantage of belt-and-pulley systems from pulley diameters. Determine output RPM, torque multiplication, and belt speed for single-stage and compound pulley drives — essential for HVAC fan systems, automotive accessories, industrial machinery, and maker projects.
🕐 Recent Calculations
What is a Pulley Ratio?
A pulley ratio describes the speed relationship between the driving (input) and driven (output) pulleys in a belt drive system, determined by the ratio of their diameters. A 6-inch driver pulley turning a 12-inch driven pulley creates a 2:1 reduction — the driven pulley rotates at half the driver speed but delivers twice the torque. This is mechanically equivalent to a gear ratio but transmitted through a belt rather than meshing teeth.
Pulley systems are used extensively in HVAC blower systems, automotive serpentine drives, industrial machinery, exercise equipment, woodworking tools, and agricultural implements. Unlike gear drives, belt-and-pulley systems can transmit power over longer distances, absorb shock loads, and slip under overload (protecting the motor), making them ideal for applications requiring vibration isolation and overload protection.
적용 수학 공식 및 방정식
이 Pulley Ratio Calculator는 5가지 핵심 수학 공식을 사용합니다:
1 Pulley Speed Ratio ▼
6-inch driver and 12-inch driven: Ratio = 6/12 = 1:2 (speed halved, torque doubled).
2 Output RPM ▼
Motor at 1750 RPM with 3" driver and 9" driven: Output = 1750 × (3/9) = 583 RPM.
3 Torque Output ▼
10 ft-lb input with 2:1 ratio: Output = 10 × 2 = 20 ft-lb (minus belt losses).
Explore all calculation options on the 비율 계산기 home page.
비율 계산기 사용법
이 비율 계산기는 아래의 3단계로 쉽게 사용할 수 있습니다:
수치 입력하기
입력 칸에 알고 있는 비율 값을 입력합니다. 구하려는 미지수 자리의 칸 하나는 비워둡니다.
모드 선택하기
비율 모드(풀기, 간소화, 스케일링)를 선택합니다. 각 모드는 입력한 수치에 맞춰 다른 공식들을 적용합니다.
결과 확인하기
계산하기 버튼을 누릅니다. 결과 화면에 정답과 함께 시각적인 비율 바, 원형 차트, 상세한 단계별 풀이 과정이 출력됩니다.
실제 예제 문제 및 단계별 풀이
비율 계산기를 활용하여 아래 3가지 예제 문제를 단계별로 해결하는 과정입니다:
입력 1 Motor: 1750 RPM, 4" driver, 10" driven pulley
입력 2 Find driver pulley size for 500 RPM output from 1200 RPM motor
입력 3 Two-stage pulley system: 3:1 then 2:1
자주 묻는 질문 (FAQ)
How do I calculate pulley RPM? ▼
Output RPM = Input RPM × (Driver Pulley Diameter ÷ Driven Pulley Diameter). A 1,750 RPM motor with a 4-inch driver and 8-inch driven pulley: Output = 1,750 × (4/8) = 875 RPM. The driven pulley turns at half the motor speed.
What determines the speed ratio in a pulley system? ▼
The ratio of the two pulley diameters. Speed Ratio = Driver Diameter ÷ Driven Diameter. A 6-inch driver and 3-inch driven = 2:1 overdrive (output turns twice as fast). A 3-inch driver and 6-inch driven = 1:2 reduction (output turns half as fast).
How do I increase the speed of a pulley-driven fan? ▼
Either increase the driver (motor) pulley diameter or decrease the driven (fan) pulley diameter. For example, changing the motor pulley from 3 inches to 4 inches increases fan speed by 33%. Alternatively, reduce the fan pulley from 8 inches to 6 inches for the same effect.
What is the difference between a pulley ratio and a gear ratio? ▼
Both describe the speed relationship between input and output. Gear ratios are determined by tooth counts (driven teeth ÷ driving teeth). Pulley ratios are determined by diameters (driver diameter ÷ driven diameter). Gears mesh directly; pulleys are connected by belts, allowing longer distance power transmission.
How does pulley ratio affect torque? ▼
Torque multiplication is the inverse of the speed ratio. A 2:1 speed reduction (output turns half as fast) doubles the output torque. A 1:2 speed increase halves the output torque. Power (speed × torque) is conserved minus belt friction losses (typically 2-5%).
What is a compound pulley system? ▼
A compound system uses two or more pulley stages in series. Each stage's ratio multiplies with the others. Stage 1: 2:1 reduction. Stage 2: 3:1 reduction. Overall: 6:1 reduction. Compound systems achieve high ratios without extremely large pulleys.
How do I calculate belt length for a two-pulley system? ▼
Belt Length ≈ 2C + π/2(D₁+D₂) + (D₁-D₂)²/(4C), where C = center distance, D₁ and D₂ are pulley diameters. For C=24 inches, D₁=6, D₂=12: L ≈ 48 + 28.27 + 0.375 ≈ 76.6 inches.
What is belt speed and why does it matter? ▼
Belt speed = π × Pulley Diameter × RPM ÷ 12 (in FPM). Standard V-belts should not exceed 6,500 FPM. Excessive speed causes vibration, heat buildup, and belt ejection. If calculated speed is too high, increase both pulley diameters proportionally.
Can I use a variable-diameter pulley for speed adjustment? ▼
Yes. Variable-pitch (adjustable) pulleys have movable sheave faces that change the effective diameter. Tightening the sheave increases the effective diameter (speeds up the driven shaft), and loosening decreases it. This is how many HVAC blowers are adjusted on site.
What causes belt slip in a pulley system? ▼
Belt slip is caused by: insufficient belt tension, overloading beyond the belt's friction capacity, oil/grease contamination, worn belt or pulley grooves, misaligned pulleys, or insufficient wrap angle. Properly tensioned belts in clean, aligned systems experience minimal slip (1-2%).
How do automotive serpentine belts relate to pulley ratios? ▼
Automotive serpentine belts drive multiple accessories (alternator, A/C compressor, power steering pump, water pump) from a single crankshaft pulley. Each accessory has a different pulley diameter to achieve its required RPM. The alternator typically uses a small pulley (2:1 to 3:1 overdrive) to spin fast enough to generate adequate power at idle.