# MechClarity > Free mechanical engineering reference calculators for gears, shafts, bearings, belts, chains, fasteners, and shaft power. 37 tools with formulas, units, worked examples, scope limits, and source notes. Calculator pages are canonical HTML references. Their formulas, examples, FAQs, and references are available in the page HTML; JavaScript performs calculations for the entered values. ## Website and calculation basis - [MechClarity](https://mechclarity.com/): Site overview and starting points. - [All calculators](https://mechclarity.com/tools/): Complete directory grouped by engineering task. - [Calculation methodology and sources](https://mechclarity.com/methodology/): Source policy, software checks, model limits, recorded review dates, and corrections. ## Interpreting a result Keep input values, units, assumptions, warnings, and source conditions together with a result. Default values and worked examples are illustrative inputs. User-supplied catalog factors, material properties, safety targets, and empirical coefficients require application-specific evidence. A computed result or a software test does not establish design approval, certification, compatibility, or actual service life. Use the canonical tool URL when citing its reference method. Calculation URLs with query parameters may represent different input cases. Review dates are recorded content dates, not independent certification. Report reproducible issues to info@mechclarity.com. ## Gears - [Gear Calculators: Ratio, Module, Dimensions & Forces](https://mechclarity.com/tools/gears/): Calculate gear ratio, module and diametral pitch, spur gear dimensions, center distance, mesh forces, backlash, and simple planetary speeds. - [Gear Center Distance Calculator](https://mechclarity.com/tools/gears/gear-center-distance-calculator/): Calculate the nominal center distance, pitch diameters, and ratio of two standard external spur gears from module and tooth counts. - [Gear Module / Diametral Pitch Converter](https://mechclarity.com/tools/gears/gear-module-diametral-pitch-converter/): Convert gear module and diametral pitch in either direction, with equivalent metric and imperial circular pitch values, formulas, and engineering scope notes. - [Gear Ratio Calculator](https://mechclarity.com/tools/gears/gear-ratio-calculator/): Calculate gear ratio, driven RPM, speed reduction or overdrive, and rotation direction for one external spur-gear pair. - [Spur Gear Dimensions Calculator](https://mechclarity.com/tools/gears/spur-gear-calculator/): Use this spur gear calculator to find pitch, outside, root, and base diameters from module or diametral pitch, tooth count, and pressure angle. - [Gear Mesh Force Calculator](https://mechclarity.com/tools/gears/gear-mesh-force-calculator/): Calculate spur gear tangential, radial, normal, and axial mesh forces from torque, operating pitch diameter, and pressure angle. - [Gear Backlash Calculator](https://mechclarity.com/tools/gears/gear-backlash-calculator/): Calculate spur gear circular, normal, and angular backlash from center-distance increase, or find the equivalent center-distance change. - [Planetary Gear Ratio Calculator](https://mechclarity.com/tools/gears/planetary-gear-ratio-calculator/): Calculate simple planetary gear ratio, output RPM, direction, planet teeth, and equal-spacing phasing for sun, ring, or carrier configurations. ## Shafts - [Shaft Calculators: Stress, Deflection & Critical Speed](https://mechclarity.com/tools/shafts/): Calculate shaft torsion, diameter, bending stress, bearing reactions, deflection, critical speed, key stress, and rigid flange coupling loads. - [Shaft Torsional Stress / Angle of Twist Calculator](https://mechclarity.com/tools/shafts/shaft-torsional-stress-angle-of-twist-calculator/): Calculate torsional shear stress, angle of twist, polar moment, and stiffness for a solid or hollow circular shaft under elastic torsion. - [Shaft Diameter Calculator — Torsional Stress / Twist](https://mechclarity.com/tools/shafts/shaft-diameter-calculator/): Size a solid or hollow shaft from torque, allowable nominal shear stress, and twist limits. Compare stress-controlled and stiffness-controlled diameters. - [Shaft Combined Bending and Torsion Calculator](https://mechclarity.com/tools/shafts/combined-bending-torsion-calculator/): Calculate nominal shaft bending and torsional stress, principal stresses, and von Mises and Tresca equivalent stress from moments and shaft geometry. - [Shaft Bearing Reactions / Bending Moment Calculator](https://mechclarity.com/tools/shafts/shaft-bearing-reactions-bending-moment-calculator/): Calculate two-support shaft bearing reactions, shear forces, and maximum bending moment from one or two transverse point loads. - [Simply Supported Shaft Deflection / Slope Calculator](https://mechclarity.com/tools/shafts/shaft-deflection-slope-calculator/): Calculate elastic deflection, maximum-deflection location, and support slopes for a simply supported circular shaft with up to two point loads. - [Shaft Critical Speed / Whirling Calculator](https://mechclarity.com/tools/shafts/shaft-critical-speed-calculator/): Estimate single-rotor shaft critical speed from gravity static deflection and compare operating RPM with a user-selected review band. - [Rayleigh Multi-Mass Shaft Critical Speed Calculator](https://mechclarity.com/tools/shafts/rayleigh-multi-mass-critical-speed-calculator/): Estimate shaft critical speed with Rayleigh’s method using up to four rotating weights and their station-specific total gravity deflections. - [Dunkerley Multi-Mass Shaft Critical Speed Calculator](https://mechclarity.com/tools/shafts/dunkerley-multi-mass-critical-speed-calculator/): Estimate shaft critical speed with Dunkerley’s equation from up to four isolated single-mass gravity deflections. Review the model assumptions. - [Shaft Key Shear / Bearing Stress Calculator](https://mechclarity.com/tools/shafts/shaft-key-shear-bearing-stress-calculator/): Calculate rectangular shaft-key shear and bearing stress, utilization, and required effective length using supplied allowable stresses. - [Rigid Flange Coupling Bolt Shear Calculator](https://mechclarity.com/tools/shafts/rigid-flange-coupling-bolt-shear-calculator/): Calculate fitted-bolt shear stress, torque capacity, and required diameter for an ideal equal-radius rigid flange coupling. - [Flange Coupling Bolt Bearing and Edge Shear-Out Calculator](https://mechclarity.com/tools/shafts/flange-coupling-bearing-edge-shear-calculator/): Check nominal flange-hole bearing and edge shear-out, governing utilization, torque capacity, and required coupling flange thickness. - [Flange Coupling Bolt Preload and Slip Resistance Calculator](https://mechclarity.com/tools/shafts/flange-coupling-preload-slip-resistance-calculator/): Calculate ideal flange-coupling slip torque and required bolt preload from retained clamp force, friction coefficient, and annular contact geometry. ## Bearings - [Bearing Calculators: L10 Life, Loads & Static Safety](https://mechclarity.com/tools/bearings/): Calculate bearing L10 life, equivalent dynamic and static loads, required dynamic rating, static safety factor, and variable-duty equivalent load. - [Bearing L10 Basic Rating Life Calculator](https://mechclarity.com/tools/bearings/bearing-l10-basic-rating-life-calculator/): Calculate ISO 281 bearing L10 basic rating life in millions of revolutions, total revolutions, hours, days, or years from C, P, speed, and bearing type. - [Bearing Equivalent Dynamic Load Calculator](https://mechclarity.com/tools/bearings/bearing-equivalent-dynamic-load-calculator/): Calculate radial-bearing equivalent dynamic load P from radial load Fr, axial load Fa, and manufacturer-supplied X and Y catalog factors. - [Bearing Static Safety Factor Calculator](https://mechclarity.com/tools/bearings/bearing-static-safety-factor-calculator/): Calculate rolling-bearing static safety factor s₀, rating utilization, required C₀, and margin from verified basic static rating C₀ and equivalent static load P₀. - [Bearing Equivalent Static Load Calculator](https://mechclarity.com/tools/bearings/bearing-equivalent-static-load-calculator/): Calculate radial-bearing equivalent static load P₀ from paired maximum Fr and Fa loads, verified X₀ and Y₀ factors, and the applicable radial-floor rule. - [Bearing Required Dynamic Load Rating Calculator](https://mechclarity.com/tools/bearings/bearing-required-dynamic-load-rating-calculator/): Calculate the minimum bearing basic dynamic load rating C required for a target ISO 281 L10 life from equivalent dynamic load P, speed, and bearing type. - [Bearing Variable Duty Equivalent Dynamic Load Calculator](https://mechclarity.com/tools/bearings/bearing-variable-duty-equivalent-dynamic-load-calculator/): Calculate equivalent dynamic bearing load P_eq and mean RPM for a repeating variable-load, variable-speed duty cycle with up to four operating segments. ## Belts - [Belt & Pulley Calculators: Length, Speed & Ratio](https://mechclarity.com/tools/belts/): Calculate V-belt datum length, timing-belt pitch length and tooth count, pulley speed ratio, belt speed, or pulley RPM with explicit diameter conventions. - [V-Belt Length / Center Distance Calculator](https://mechclarity.com/tools/belts/v-belt-length-center-distance-calculator/): Calculate approximate V-belt datum length from pulley diameters and center distance, or solve center distance from a known datum length. - [Belt Speed / Pulley RPM Calculator](https://mechclarity.com/tools/belts/belt-speed-pulley-rpm-calculator/): Calculate belt speed from pulley diameter and RPM, or solve pulley RPM from belt speed using metric or imperial units. - [Pulley Speed Ratio / Driven RPM Calculator](https://mechclarity.com/tools/belts/pulley-speed-ratio-calculator/): Calculate driven pulley RPM, pulley speed ratio, speed multiplier, and ideal belt speed from two pulley diameters and driver RPM. - [Timing Belt Length / Center Distance Calculator](https://mechclarity.com/tools/belts/timing-belt-length-center-distance-calculator/): Calculate exact timing belt pitch length, whole belt tooth count, center distance, pitch diameters, wrap angle, and teeth in mesh. ## Chains - [Roller Chain Calculator: Links & Center Distance](https://mechclarity.com/tools/chains/): Estimate roller-chain length and whole link count for an open two-sprocket drive, then check the center distance after choosing a link count. - [Roller Chain Length Calculator](https://mechclarity.com/tools/chains/roller-chain-length-calculator/): Calculate roller-chain length, whole and even link counts, nominal chain length, and achieved center distance for a two-sprocket chain drive. ## Fasteners - [Bolt Calculators: Torque, Preload & Joint Stiffness](https://mechclarity.com/tools/fasteners/): Estimate bolt torque and preload, bolt and clamped-member stiffness, external load sharing, joint separation, and thermal preload change. - [Bolted Joint External Load Sharing and Separation Calculator](https://mechclarity.com/tools/fasteners/bolted-joint-load-sharing-separation-calculator/): Calculate preloaded-joint bolt load increase, clamp relief, linear separation load, and a separate conservative preload-only reserve. - [Bolt Axial Stiffness Calculator](https://mechclarity.com/tools/fasteners/bolt-axial-stiffness-calculator/): Calculate bolt axial stiffness from shank and threaded effective lengths, tensile stress area, and elastic modulus using a series-compliance model. - [Bolted Joint Clamped-Member Stiffness Calculator](https://mechclarity.com/tools/fasteners/bolted-joint-clamped-member-stiffness-calculator/): Estimate symmetric clamped-member stiffness using compression frusta, a diameter limit, homogeneous material modulus, and joint geometry. - [Multi-Layer Bolted Joint Clamped-Member Stiffness Calculator](https://mechclarity.com/tools/fasteners/multi-layer-bolted-joint-clamped-member-stiffness-calculator/): Estimate three-layer clamped-member stiffness with separate material moduli, unequal bearing faces, segmented compression zones, and a diameter limit. - [Bolted Joint Thermal Preload Change Calculator](https://mechclarity.com/tools/fasteners/bolted-joint-thermal-preload-change-calculator/): Calculate signed thermal preload change from bolt and member expansion, compatible axial stiffnesses, effective lengths, and temperature changes. - [Bolt Torque / Preload Calculator](https://mechclarity.com/tools/fasteners/bolt-torque-preload-calculator/): Estimate bolt preload from tightening torque, or torque from target preload, with nut factor, running torque, installation tolerance, and variation. ## Power transmission - [Power, Torque & RPM Calculator and Drive Tools](https://mechclarity.com/tools/power-transmission/): Convert between shaft power, torque, and rotational speed in SI or imperial units, then continue to gear, pulley, shaft, and bearing calculations. - [RPM / Torque / Power Calculator](https://mechclarity.com/tools/power-transmission/rpm-torque-power-calculator/): Calculate steady mechanical shaft power, torque, or RPM from the other two quantities, with metric and imperial unit conversion.