Gear Ratio Calculator (i=z₂/z₁)
Compute the gear ratio via i = z₂/z₁: enter driving/driven tooth counts and input speed to get ratio, output speed and torque multiplication.
Key points
Gear Ratio Calculator (i=z₂/z₁): Compute the gear ratio via i = z₂/z₁: enter driving/driven tooth counts and input speed to get ratio, output speed and torque multiplication. Formula: i = z₂/z₁ = n₁/n₂ = τ₂/τ₁. Enter parameters on the DD-CAT IDE online tool page to get results instantly, with a calculation-model diagram that updates with the inputs. i = z₂/z₁ = n₁/n₂: the tooth-count ratio sets the gear ratio; i > 1 reduces speed and increases torque, i < 1 increases speed and reduces torque. Speed and torque: n₂ = n₁/i, τ₂ = τ₁·i (ideal, lossless); real output torque must be multiplied by transmission efficiency η (0.9–0.98).
Inputs
i = z₂/z₁ = n₁/n₂ = τ₂/τ₁Calculation model (updates with parameters)
| Gear ratio i | 3 | i = z₂/z₁ |
| Output speed n₂ | 500rpm | n₂ = n₁/i |
| Output torque τ₂ | 150N·m | τ₂ = τ₁·i (ignoring efficiency loss) |
| Rotation direction | Same (external single-stage meshing reverses) | 外啮合每级反向；内啮合 / 惰轮改变 |
Engineering notes
- i = z₂/z₁ = n₁/n₂: the tooth-count ratio sets the gear ratio; i > 1 reduces speed and increases torque, i < 1 increases speed and reduces torque.
- Speed and torque: n₂ = n₁/i, τ₂ = τ₁·i (ideal, lossless); real output torque must be multiplied by transmission efficiency η (0.9–0.98).
- The total ratio of multi-stage gearing is the product of the stages; each external mesh reverses direction, while idlers change direction without altering the ratio.
FAQ
- What is Gear Ratio Calculator (i=z₂/z₁) for?
- Compute the gear ratio via i = z₂/z₁: enter driving/driven tooth counts and input speed to get ratio, output speed and torque multiplication.
- What is the formula for Gear Ratio Calculator (i=z₂/z₁)?
- Core formula: i = z₂/z₁ = n₁/n₂ = τ₂/τ₁. The tool returns results instantly using this formula and the selected parameters.
- What engineering notes should I keep in mind when using Gear Ratio Calculator (i=z₂/z₁)?
- i = z₂/z₁ = n₁/n₂: the tooth-count ratio sets the gear ratio; i > 1 reduces speed and increases torque, i < 1 increases speed and reduces torque. Speed and torque: n₂ = n₁/i, τ₂ = τ₁·i (ideal, lossless); real output torque must be multiplied by transmission efficiency η (0.9–0.98). The total ratio of multi-stage gearing is the product of the stages; each external mesh reverses direction, while idlers change direction without altering the ratio.