Gear Ratio Calculator
Calculate gear ratio accurately for your build. Get material quantities, waste allowances, and project cost breakdowns.
Calculator
Adjust values & calculateThe gear connected to the power source
The gear connected to the output/load
Formula
The gear ratio equals the number of teeth on the driven gear divided by the driving gear teeth. Output RPM is inversely proportional to the ratio, while output torque is directly proportional (multiplied by the efficiency factor ฮท). Power is conserved minus friction losses.
Last reviewed: December 2025
Worked Examples
Example 1: Motor Speed Reduction
Example 2: Bicycle Gear Analysis
Background & Theory
The Gear Ratio Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads โ the permanent self-weight of structural elements, finishes, and fixed equipment โ and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40โ0.45 typically yields concrete with 28-day compressive strengths of 30โ40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5โ2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250โ350 MPa for mild steel) and ultimate tensile strength (typically 400โ500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by ฮด = FLยณ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of mยฒยทK/W (SI) or ftยฒยทยฐFยทh/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1โ2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.
History
The history behind the Gear Ratio Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete โ a mixture of volcanic ash, lime, and seawater โ enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including Franรงois Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes โ including the 1971 San Fernando and 1994 Northridge events โ drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.
Key Features
- Estimate total fuel cost for any road trip by entering distance, vehicle fuel efficiency, and current fuel price, with support for both imperial and metric units.
- Compare two tire sizes side by side to calculate the difference in overall diameter, section width, and sidewall height, and determine the speedometer correction factor when changing tire sizes.
- Convert engine power output between horsepower and kilowatts, and convert torque between pound-feet and Newton-metres, for accurate cross-market vehicle specification comparisons.
- Calculate braking stopping distance at any speed for dry, wet, or icy road conditions using standard deceleration rates, helping drivers understand safe following distances.
- Project vehicle depreciation over any ownership period using declining-balance or straight-line methods, and estimate the residual trade-in or resale value at a future date.
- Run a total-cost-of-ownership break-even analysis comparing an electric vehicle against a petrol equivalent, factoring in purchase price difference, fuel savings, and charging costs over time.
- Calculate engine RPM at a given road speed for any gear ratio, final drive ratio, and tyre circumference, useful for evaluating gearing changes or custom differential setups.
- Verify towing capacity against trailer weight and calculate tongue load, payload distribution across axles, and whether the combined gross vehicle weight rating is within legal limits.
Frequently Asked Questions
Formula
Gear Ratio = Driven Teeth / Driving Teeth | Output RPM = Input RPM / Ratio | Output Torque = Input Torque ร Ratio ร ฮท
The gear ratio equals the number of teeth on the driven gear divided by the driving gear teeth. Output RPM is inversely proportional to the ratio, while output torque is directly proportional (multiplied by the efficiency factor ฮท). Power is conserved minus friction losses.
Worked Examples
Example 1: Motor Speed Reduction
Problem: A 1750 RPM motor with a 15-tooth pinion drives a 75-tooth gear. The motor produces 10 Nยทm of torque. Calculate outputs at 95% efficiency.
Solution: Gear Ratio = 75/15 = 5:1\nOutput RPM = 1750 / 5 = 350 RPM\nOutput Torque = 10 ร 5 ร 0.95 = 47.5 Nยทm\nInput Power = 10 ร 1750 ร 2ฯ/60 = 1,832.6W = 2.46HP\nOutput Power = 1,832.6 ร 0.95 = 1,740.9W
Result: Ratio = 5:1 | Output = 350 RPM | Torque = 47.5 Nยทm | 2.46HP
Example 2: Bicycle Gear Analysis
Problem: A bicycle has a 44-tooth chainring driving a 16-tooth rear sprocket. The cyclist pedals at 80 RPM with 40 Nยทm of torque.
Solution: Gear Ratio = 16/44 = 0.364 (speed increase)\nOutput RPM = 80 / 0.364 = 220 RPM (wheel turns faster)\nOutput Torque = 40 ร 0.364 ร 0.97 = 14.1 Nยทm\nThis is a speed-increasing setup (ratio < 1)\nWheel turns 2.75ร faster than pedals
Result: Ratio = 0.364:1 | Wheel = 220 RPM | Torque = 14.1 Nยทm
Frequently Asked Questions
What is a gear ratio?
A gear ratio is the relationship between the number of teeth on two meshing gears, expressed as the ratio of driven gear teeth to driving gear teeth. It determines how speed and torque are transferred between gears. A gear ratio greater than 1 means speed reduction and torque multiplication (the output shaft turns slower but with more force). A gear ratio less than 1 means speed increase and torque reduction. For example, a 60-tooth driven gear meshing with a 20-tooth driving gear gives a 3:1 ratio, meaning the output turns 3 times slower but with 3 times the torque.
How does gear ratio affect torque and speed?
Gear ratio creates an inverse relationship between speed and torque: Speed reduction = torque multiplication, and speed increase = torque reduction. Output RPM = Input RPM / Gear Ratio. Output Torque = Input Torque x Gear Ratio x Efficiency. In an ideal (100% efficient) system, power is conserved: P = Torque x RPM. In reality, friction losses reduce efficiency to typically 95-98% per gear stage. This trade-off is fundamental to mechanical design, allowing engineers to match motor characteristics to load requirements.
What is the difference between gear ratio and speed ratio?
Gear ratio and speed ratio are reciprocals of each other. Gear ratio = Driven teeth / Driving teeth = Input speed / Output speed. Speed ratio = Driving teeth / Driven teeth = Output speed / Input speed. For example, if a 20-tooth gear drives a 60-tooth gear: Gear ratio = 60/20 = 3:1 (output is 3x slower), Speed ratio = 20/60 = 1:3 (output is 1/3 the speed). Engineers typically use gear ratio when discussing torque multiplication and speed ratio when discussing velocity changes.
How do I calculate compound gear train ratios?
For a compound gear train (multiple gear pairs on shared shafts), the overall gear ratio is the product of individual pair ratios. For a two-stage train: Total Ratio = (Driven1/Driving1) x (Driven2/Driving2). For example: Stage 1: 20-tooth drives 60-tooth (3:1), Stage 2: 15-tooth drives 45-tooth (3:1). Total ratio = 3 x 3 = 9:1. The output turns 9 times slower with 9 times the torque. Compound trains allow high ratios in compact space. Each stage adds friction losses (typically 2-5% per mesh), so a 3-stage train at 97% per stage has 91.3% overall efficiency.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
References
Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy