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RC Hobby Math Center

Planes, boats, cars, trucks, drones, helicopters, batteries, motors, gearing, scale models and race planning. 150 tools with purposes, formulas and worked examples.

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All 150 tools: purposes and formulas

RC plane flight-time estimate — Estimate runtime from capacity and measured average current.
Minutes = mAh/1000 × usable share / average amps × 60
RC boat runtime estimate — Estimate runtime from capacity and measured average current.
Minutes = mAh/1000 × usable share / average amps × 60
RC car runtime estimate — Estimate runtime from capacity and measured average current.
Minutes = mAh/1000 × usable share / average amps × 60
RC truck runtime estimate — Estimate runtime from capacity and measured average current.
Minutes = mAh/1000 × usable share / average amps × 60
Drone flight-time estimate — Estimate runtime from capacity and measured average current.
Minutes = mAh/1000 × usable share / average amps × 60
RC plane no-load motor RPM — Estimate unloaded motor speed from Kv and voltage.
No-load RPM ≈ motor Kv × voltage
RC boat no-load motor RPM — Estimate unloaded motor speed from Kv and voltage.
No-load RPM ≈ motor Kv × voltage
RC car no-load motor RPM — Estimate unloaded motor speed from Kv and voltage.
No-load RPM ≈ motor Kv × voltage
RC truck no-load motor RPM — Estimate unloaded motor speed from Kv and voltage.
No-load RPM ≈ motor Kv × voltage
Drone no-load motor RPM — Estimate unloaded motor speed from Kv and voltage.
No-load RPM ≈ motor Kv × voltage
Plane propeller pitch-speed illustration — Translate pitch and RPM into ideal advance with an entered slip assumption.
Speed m/s = pitch inches × 0.0254 × RPM/60 × (1 − slip/100)
Boat propeller pitch-speed illustration — Translate pitch and RPM into ideal advance with an entered slip assumption.
Speed m/s = pitch inches × 0.0254 × RPM/60 × (1 − slip/100)
Plane advance-speed assumption — Translate pitch and RPM into ideal advance with an entered slip assumption.
Speed m/s = pitch inches × 0.0254 × RPM/60 × (1 − slip/100)
RC racing boat advance-speed assumption — Translate pitch and RPM into ideal advance with an entered slip assumption.
Speed m/s = pitch inches × 0.0254 × RPM/60 × (1 − slip/100)
Airboat propeller pitch-speed illustration — Translate pitch and RPM into ideal advance with an entered slip assumption.
Speed m/s = pitch inches × 0.0254 × RPM/60 × (1 − slip/100)
Plane wing loading — Compare flying mass with projected wing area.
Wing loading = flying grams / wing dm²
Rectangular model wing area — Calculate a rectangular wing planform.
Area dm² = span cm × chord cm / 100
Tapered wing planform area — Estimate a straight tapered wing with two chord lengths.
Area dm² = span × (root chord + tip chord)/2 / 100
Model wing aspect ratio — Relate span to projected wing area.
Aspect ratio = span² / wing area
CG position as chord percentage — Describe a measured CG location relative to reference chord.
CG percent = distance / reference chord × 100
Boat displaced water volume — Model static volume displaced by a floating boat.
Displaced liters = mass / density × 1000
Boat sealed-volume buoyancy illustration — Calculate fluid mass corresponding to entered sealed displaced volume.
Displaced mass kg = liters/1000 × density
Scale boat waterline length — Convert full-size waterline length to model size.
Model length mm = full-size meters × 1000 / scale denominator
Boat prop-shaft RPM with reduction — Calculate shaft RPM through a mechanical reduction.
Shaft RPM = motor RPM / reduction ratio
Boat circular turn time geometry — Estimate time around a circular path.
Seconds = 2π × radius / speed
RC car final drive ratio — Combine spur/pinion gearing with internal reduction.
Final ratio = spur teeth / pinion teeth × internal reduction
RC truck final drive ratio — Combine spur/pinion gearing with internal reduction.
Final ratio = spur teeth / pinion teeth × internal reduction
Crawler final drive ratio — Combine spur/pinion gearing with internal reduction.
Final ratio = spur teeth / pinion teeth × internal reduction
Buggy final drive ratio — Combine spur/pinion gearing with internal reduction.
Final ratio = spur teeth / pinion teeth × internal reduction
Monster truck final drive ratio — Combine spur/pinion gearing with internal reduction.
Final ratio = spur teeth / pinion teeth × internal reduction
RC car theoretical gearing speed — Relate loaded motor RPM, final ratio and rolling tire diameter.
km/h = π × diameter_mm/1000 × motor_RPM/final_ratio × 60/1000
RC truck theoretical gearing speed — Relate loaded motor RPM, final ratio and rolling tire diameter.
km/h = π × diameter_mm/1000 × motor_RPM/final_ratio × 60/1000
Crawler theoretical gearing speed — Relate loaded motor RPM, final ratio and rolling tire diameter.
km/h = π × diameter_mm/1000 × motor_RPM/final_ratio × 60/1000
Buggy theoretical gearing speed — Relate loaded motor RPM, final ratio and rolling tire diameter.
km/h = π × diameter_mm/1000 × motor_RPM/final_ratio × 60/1000
Monster truck theoretical gearing speed — Relate loaded motor RPM, final ratio and rolling tire diameter.
km/h = π × diameter_mm/1000 × motor_RPM/final_ratio × 60/1000
Pinion-change RPM factor — Compare wheel speed factors after changing pinion tooth count.
Wheel-speed factor = new pinion / old pinion
Spur-change RPM factor — Compare wheel speed factors after changing spur tooth count.
Wheel-speed factor = old spur / new spur
Tire rollout per motor revolution — Calculate vehicle travel per motor turn.
Rollout mm = π × tire diameter / final ratio
Metric gear center-distance geometry — Calculate nominal centers for two external spur gears.
Center distance = module × (teeth A + teeth B)/2
Ideal gear output torque — Model torque multiplication through a reduction.
Output torque = input torque × reduction ratio × efficiency
Series pack nominal voltage — Add nominal voltage across series cells.
Pack voltage = series cells × nominal cell voltage
Parallel-cell capacity arithmetic — Add identical rated capacities in parallel.
Pack capacity = cell capacity × parallel count
RC pack nominal energy — Compare packs by rated watt-hours.
Nominal Wh = mAh/1000 × nominal voltage
Advertised C-rating current arithmetic — Translate a stated C rating into its claimed current.
Stated current A = capacity Ah × stated C rating
Specified charge-C current arithmetic — Convert a manufacturer-approved charge rate into amps.
Charge current A = capacity Ah × approved charge C
Ideal constant-current charge time — Estimate time to replace a known discharged capacity.
Ideal minutes = mAh/1000 / amps × 60
Charger DC input power model — Estimate DC input draw for an output charging power.
Input watts = output watts / efficiency
Charging session energy model — Estimate energy delivered at average charge power.
Energy Wh = average watts × minutes/60
RC charging electricity cost — Calculate cost from measured wall energy.
Cost = measured kWh × price/kWh
Capacity remaining from logged discharge — Subtract measured discharged capacity from a capacity budget.
Remaining mAh = capacity budget − logged discharge
Measured RC electrical input power — Calculate input power from measured voltage and current.
Input watts = measured volts × measured amps
Motor shaft-power assumption — Apply an entered efficiency to measured input power.
Output watts = input watts × efficiency
Plane electrical power per flying mass — Normalize measured electrical power by model mass.
Electrical power loading = input watts / flying kg
Measured current share of ESC rating — Compare logged current with the entered continuous rating.
Rating share % = measured amps / entered rating × 100
Shaft torque from power and RPM — Calculate torque for measured mechanical shaft power.
Torque N·m = shaft watts / (RPM × 2π/60)
DC wiring voltage drop — Use measured total loop resistance and current.
Voltage drop = current × total loop resistance
Wiring heat-loss power — Model resistive loss in an entered circuit loop.
Loss watts = current² × loop resistance
Battery resistance sag model — Estimate resistive voltage sag from entered pack resistance.
Sag volts = amps × milliohms/1000
Connector dissipation model — Calculate resistive loss across an entered connector resistance.
Loss watts = amps² × milliohms/1000
Receiver BEC output power — Calculate DC output power from measured receiver load.
Output watts = bus volts × measured amps
Servo arm force illustration — Relate rated torque to force at a lever radius.
Ideal force kgf = torque kgf·cm / arm radius cm
Servo arm tip arc travel — Compute arc travel from arm radius and rotation.
Arc travel mm = radius × angle × π/180
Servo arm tip chord travel — Compute straight displacement between two arm angles.
Chord mm = 2 × radius × sin(angle/2)
Servo transit-time estimate — Scale a stated seconds-per-60-degree speed.
Time seconds = rated seconds/60° × angle/60
Ideal linkage lever ratio — Compare servo and control horn radii.
Small-angle surface rotation factor = servo radius / horn radius
Full-size length to scale model — Convert full-size geometry at 1:N scale.
Model mm = full-size meters × 1000 / N
Full-size plane wingspan to model — Convert full-size geometry at 1:N scale.
Model mm = full-size meters × 1000 / N
Full-size boat length to model — Convert full-size geometry at 1:N scale.
Model mm = full-size meters × 1000 / N
Model length to full-size equivalent — Recover full-size length from a model measurement.
Full-size meters = model mm × N / 1000
Geometric scale volume factor — See how volume scales with length.
Full-size/model volume factor = N³
Average lap time — Average a completed race time across completed laps.
Average seconds/lap = race seconds / laps
Average lap speed — Translate lap length and time into an average speed.
Average km/h = lap meters / lap seconds × 3.6
Whole laps in a time window — Estimate full laps at a constant lap time.
Whole laps = floor(session seconds / lap seconds)
Lap-time improvement percentage — Compare old and new lap times.
Improvement % = (old − new)/old × 100
Battery energy per completed lap — Normalize measured energy use by lap count.
Wh/lap = measured energy / laps
Measured thrust-to-weight ratio — Compare total measured static thrust with flying weight.
Thrust/weight = measured thrust gf / mass g
Equal-share hover thrust illustration — Divide model weight equally among motors.
Static hover share gf/motor = mass grams / motors
Total rotor disk area — Add circular disk areas for equal rotors.
Total area = count × π × (diameter inches × 0.0254/2)²
Drone mass per rotor disk area — Normalize flying mass by total rotor disk area.
Mass disk loading = kg / total disk area
Drone route energy from measured use — Scale logged watt-hours per minute to flight minutes.
Energy Wh = measured Wh/minute × minutes
Helicopter head speed from gearing — Translate loaded motor RPM to main rotor RPM.
Main rotor RPM = motor RPM × pinion/main teeth
Helicopter blade-tip speed — Calculate geometric blade-tip tangential speed.
Tip m/s = 2π × radius × RPM/60
Main rotor disk area — Calculate projected circular rotor disk area.
Area = π × radius²
Helicopter mass disk loading — Relate flying mass to main rotor disk area.
Mass loading = kg / (π × radius²)
Tail rotor RPM from drive ratio — Apply a known main-to-tail speed ratio.
Tail RPM = main rotor RPM × drive ratio
Propeller disk area — Calculate circular swept disk area.
Area = π × (inches × 0.0254/2)²
Model compartment volume — Estimate a rectangular internal compartment.
Volume liters = length × width × height / 1000
Wing dihedral geometry — Find an angle from tip rise and horizontal half-span.
Angle = atan(rise/run) × 180/π
Control surface arc throw — Convert rotation angle to tip arc movement.
Arc throw mm = hinge radius × angle × π/180
RC all-up mass budget — Add airframe/hull/chassis, electronics and battery masses.
All-up grams = structure + electronics + battery + other
Complete RC build budget — Add structure, electronics, power pack and extras.
Total = kit + electronics + power items + extras
RC repair parts total — Sum parts and shipping costs.
Total = parts + shipping + other
Battery purchase cost per session — Spread pack purchase cost across an assumed number of usable sessions.
Cost per session = purchase cost / sessions
Monthly RC hobby budget — Add parts, track fees, travel and other hobby spending.
Monthly total = parts + fees + travel + other
Race event cost per entrant — Share a fixed event budget across entrants.
Budget per entrant = total budget / entrants
Model measured ground speed — Use timed travel over a measured distance.
Measured km/h = distance/time × 3.6
Measured motor efficiency — Compare mechanical output with electrical input.
Efficiency % = mechanical output / electrical input × 100
Logged capacity budget used — Compare discharged mAh with an entered capacity budget.
Used share % = discharged mAh / capacity budget × 100
Loaded versus no-load RPM reduction — Compare measured loaded RPM to a no-load reference.
RPM reduction % = (reference − loaded)/reference × 100
Measured pack energy per mass — Normalize delivered energy by pack mass.
Delivered energy density = delivered Wh / pack kg
Horizontal tail volume coefficient — Horizontal tail volume coefficient using your entered measurements and assumptions.
Result = ((A × B) ÷ (C × D)); A = Tail area cm², B = Tail moment arm cm, C = Wing area cm², D = Mean wing chord cm
Vertical tail volume coefficient — Vertical tail volume coefficient using your entered measurements and assumptions.
Result = ((A × B) ÷ (C × D)); A = Fin area cm², B = Fin moment arm cm, C = Wing area cm², D = Wing span cm
Tapered wing mean aerodynamic chord — Tapered wing mean aerodynamic chord using your entered measurements and assumptions.
Result = ((((A × 2) ÷ 3) × ((1 + B) + (B × B))) ÷ (1 + B)); A = Root chord cm, B = Taper ratio
Tapered wing MAC span station — Tapered wing MAC span station using your entered measurements and assumptions.
Result = (((A ÷ 6) × (1 + (B × 2))) ÷ (1 + B)); A = Full wing span cm, B = Taper ratio
Elevator chord share — Elevator chord share using your entered measurements and assumptions.
Result = ((A ÷ B) × 100); A = Elevator chord cm, B = Local stabilizer chord cm
Rudder chord share — Rudder chord share using your entered measurements and assumptions.
Result = ((A ÷ B) × 100); A = Rudder chord cm, B = Local fin chord cm
Wing skin material mass — Wing skin material mass using your entered measurements and assumptions.
Result = ((A × B) × C); A = Skin area cm², B = Thickness cm, C = Material density g/cm³
Cut rib set mass — Cut rib set mass using your entered measurements and assumptions.
Result = (((A × B) × C) × D); A = Single rib area cm², B = Thickness cm, C = Density g/cm³, D = Rib count
Rectangular spar mass — Rectangular spar mass using your entered measurements and assumptions.
Result = (((A × B) × C) × D); A = Length cm, B = Width cm, C = Height cm, D = Density g/cm³
Covering film mass — Covering film mass using your entered measurements and assumptions.
Result = (A × B); A = Applied area m², B = Film areal mass g/m²
Rectangular waterline displacement estimate — Rectangular waterline displacement estimate using your entered measurements and assumptions.
Result = (((A × B) × C) ÷ 1000); A = Waterline length cm, B = Waterline width cm, C = Immersed depth cm
Draft change for added mass — Draft change for added mass using your entered measurements and assumptions.
Result = (((A ÷ B) × 1000) ÷ C); A = Added mass kg, B = Water density kg/L, C = Waterplane area cm²
Ballast lever moment — Ballast lever moment using your entered measurements and assumptions.
Result = (A × B); A = Ballast mass grams, B = Horizontal lever cm
Boat shaft angle from rise and run — Boat shaft angle from rise and run using your entered measurements and assumptions.
Result = ((atan((A ÷ B)) × 180) ÷ π); A = Vertical shaft rise mm, B = Horizontal shaft run mm
Rectangular hatch gasket length — Rectangular hatch gasket length using your entered measurements and assumptions.
Result = ((A + B) × 2); A = Hatch length cm, B = Hatch width cm
Hull sheet mass estimate — Hull sheet mass estimate using your entered measurements and assumptions.
Result = ((A × B) × C); A = Sheet surface area cm², B = Thickness cm, C = Density g/cm³
Two component longitudinal balance — Two component longitudinal balance using your entered measurements and assumptions.
Result = (((A × B) + (C × D)) ÷ (A + C)); A = Component A mass g, B = A station cm, C = Component B mass g, D = B station cm
Boat rudder linkage ratio — Boat rudder linkage ratio using your entered measurements and assumptions.
Result = (A ÷ B); A = Servo arm radius mm, B = Rudder arm radius mm
Measured bilge pump volume — Measured bilge pump volume using your entered measurements and assumptions.
Result = (A × B); A = Measured pump rate L/min, B = Operating minutes
Measured cooling water flow — Measured cooling water flow using your entered measurements and assumptions.
Result = ((A ÷ B) × 60); A = Collected volume mL, B = Collection time seconds
RC speedometer signed error — RC speedometer signed error using your entered measurements and assumptions.
Result = (((A - B) ÷ B) × 100); A = Reported speed km/h, B = Reference measured speed km/h
Measured drivetrain rollout — Measured drivetrain rollout using your entered measurements and assumptions.
Result = (A ÷ B); A = Tire circumference mm, B = Motor turns per wheel turn
Wheel outside track width — Wheel outside track width using your entered measurements and assumptions.
Result = (A + B); A = Center-to-center wheel width mm, B = Tire width mm
Ride-height change from tire radius — Ride-height change from tire radius using your entered measurements and assumptions.
Result = ((A - B) ÷ 2); A = New tire diameter mm, B = Old tire diameter mm
Measured linear spring rate — Measured linear spring rate using your entered measurements and assumptions.
Result = (A ÷ B); A = Additional force N, B = Additional compression mm
Two parallel spring rates — Two parallel spring rates using your entered measurements and assumptions.
Result = (A + B); A = Spring A N/mm, B = Spring B N/mm
Two series spring rates — Two series spring rates using your entered measurements and assumptions.
Result = ((A × B) ÷ (A + B)); A = Spring A N/mm, B = Spring B N/mm
Race gap from average lap times — Race gap from average lap times using your entered measurements and assumptions.
Result = ((A - B) × C); A = Opponent lap seconds, B = Your lap seconds, C = Completed laps
Pit stop lap saving break-even — Pit stop lap saving break-even using your entered measurements and assumptions.
Result = ceil((A ÷ B)); A = Pit stop seconds, B = Time saved per later lap seconds
Measured tire diameter wear rate — Measured tire diameter wear rate using your entered measurements and assumptions.
Result = ((A - B) ÷ C); A = Starting diameter mm, B = Current diameter mm, C = Runs completed
Battery loaded voltage sag — Battery loaded voltage sag using your entered measurements and assumptions.
Result = (A - B); A = Resting voltage V, B = Loaded voltage V
Pack effective resistance from sag — Pack effective resistance from sag using your entered measurements and assumptions.
Result = (((A - B) ÷ C) × 1000); A = Resting voltage V, B = Loaded voltage V, C = Measured current A
Connector measured voltage drop — Connector measured voltage drop using your entered measurements and assumptions.
Result = (A - B); A = Upstream voltage V, B = Downstream voltage V
Connector measured power loss — Connector measured power loss using your entered measurements and assumptions.
Result = (A × B); A = Measured connector drop V, B = Current A
Returned charge share — Returned charge share using your entered measurements and assumptions.
Result = ((A ÷ B) × 100); A = Returned charge mAh, B = Nominal capacity mAh
Wattmeter percentage error — Wattmeter percentage error using your entered measurements and assumptions.
Result = (((A - B) ÷ B) × 100); A = Wattmeter power W, B = Reference power W
Measured flight energy per distance — Measured flight energy per distance using your entered measurements and assumptions.
Result = (A ÷ B); A = Consumed energy Wh, B = Recorded distance km
Measured boat energy per distance — Measured boat energy per distance using your entered measurements and assumptions.
Result = (A ÷ B); A = Consumed energy Wh, B = Recorded distance km
Measured car energy per distance — Measured car energy per distance using your entered measurements and assumptions.
Result = (A ÷ B); A = Consumed energy Wh, B = Recorded distance km
RC pack inventory nominal energy — RC pack inventory nominal energy using your entered measurements and assumptions.
Result = (A × B); A = Energy per pack Wh, B = Number of packs
Servo command interval share — Servo command interval share using your entered measurements and assumptions.
Result = ((A ÷ B) × 100); A = Pulse change microseconds, B = Configured full span microseconds
Measured servo angular speed — Measured servo angular speed using your entered measurements and assumptions.
Result = (A ÷ B); A = Measured movement degrees, B = Elapsed seconds
Servo arm arc length — Servo arm arc length using your entered measurements and assumptions.
Result = (((A × B) × π) ÷ 180); A = Arm radius mm, B = Rotation degrees
Servo arm endpoint chord travel — Servo arm endpoint chord travel using your entered measurements and assumptions.
Result = ((A × 2) × sin(((B × π) ÷ 360))); A = Arm radius mm, B = Rotation degrees
Measured servo current total — Measured servo current total using your entered measurements and assumptions.
Result = (A × B); A = Measured current per servo A, B = Simultaneously active servos
Receiver bench runtime estimate — Receiver bench runtime estimate using your entered measurements and assumptions.
Result = (A ÷ B); A = Usable receiver battery mAh, B = Measured average draw mA
Two-item balance shift moment — Two-item balance shift moment using your entered measurements and assumptions.
Result = ((A × B) - (C × D)); A = Added mass g, B = Added station cm, C = Removed mass g, D = Removed station cm
Geometrically similar model volume ratio — Geometrically similar model volume ratio using your entered measurements and assumptions.
Result = (A ^ 3); A = Linear scale factor
Airframe material budget — Airframe material budget using your entered measurements and assumptions.
Result = (((A + B) + C) + D); A = Sheet cost, B = Hardware cost, C = Covering cost, D = Adhesive cost
RC event pack cycles estimate — RC event pack cycles estimate using your entered measurements and assumptions.
Result = ceil((A ÷ B)); A = Planned runs, B = Runs per charged pack

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