# Robotics Formula Cheat Sheet: Free Printable

> Free cheat sheet of robotics formulas with worked examples: Ohm law, batteries, gears, wheels, encoders and steppers.

Canonical: https://roboticsengineering.in/free-library/robotics-formula-cheat-sheet/ | Published: 2026-11-04 | Updated: 2026-11-04

**The formulas you reach for most when building a robot, with one worked example each.** Every number below was recomputed by hand. Examples use assumed values, not measurements from a build, so replace them with your own parts.

## Electricity

- Ohm’s law: V = I x R. Power: P = V x I = I x I x R = V x V / R.
- LED resistor: R = (supply voltage – LED voltage) / LED current. Example: (5 – 2) / 0.010 = 300 ohm.
- Voltage divider: Vout = Vin x R2 / (R1 + R2). Example: 5 V with 1 k and 2 k gives 5 x 2000 / 3000 = 3.33 V.
- Heat in a wire or joint: P = I x I x R. Example: 5 A through 0.05 ohm is 5 x 5 x 0.05 = 1.25 W.
- PWM average voltage: duty cycle x supply. Example: 60 percent of 12 V is 7.2 V.

Check any result with the [Ohm’s law and power calculator](https://roboticsengineering.in/ohms-law-power-calculator/) and the [LED resistor and voltage divider calculator](https://roboticsengineering.in/led-resistor-voltage-divider-calculator/).

## Batteries

- Energy in watt-hours = volts x amp-hours.
- Runtime in hours = energy x usable fraction / load in watts.
- Example: 11.1 V x 2.2 Ah = 24.42 Wh. Using 80 percent gives 19.5 Wh. At a 10 W load that is 19.5 / 10 = about 1.95 hours.
- Series adds voltage, parallel adds capacity. Example: 3s2p of 3.7 V, 2.5 Ah cells is 11.1 V, 5 Ah and 55.5 Wh.
- Fuse size: load current x 1.25 for a continuous load, then round up to the next standard size, never above what the wire can carry.

Try the [battery runtime calculator](https://roboticsengineering.in/robot-battery-runtime-calculator/) and the [battery pack calculator](https://roboticsengineering.in/battery-pack-series-parallel-calculator/).

## Motors, wheels and gears

- Wheel speed = pi x diameter x revolutions per second. Example: 65 mm wheel at 2 rev/s is 3.1416 x 0.065 x 2 = 0.408 m/s.
- Torque = force x distance. Example: a 0.5 kg load at 0.2 m is 0.5 x 9.81 x 0.2 = 0.981 N m, about 10 kgf cm. Add a safety margin before choosing a motor.
- Gear ratio = driven teeth / driver teeth. Output speed = input speed / ratio. Output torque is about input torque x ratio x efficiency. Example: a 20 tooth gear driving a 60 tooth gear gives ratio 3, so 300 rpm becomes 100 rpm.
- Encoder distance per count = pi x diameter / counts per wheel revolution. Example: 65 mm wheel, 20 counts per revolution: 204.2 / 20 = 10.2 mm per count.
- Stepper step rate = revolutions per second x steps per revolution. Example: 200 full steps with 16x microstepping is 3200 steps per revolution; at 120 rpm (2 rev/s) that is 6400 steps per second.

Use the [wheel speed calculator](https://roboticsengineering.in/wheel-speed-rpm-calculator/), [servo torque calculator](https://roboticsengineering.in/servo-torque-calculator/), [gear train calculator](https://roboticsengineering.in/gear-train-calculator/), [encoder calculator](https://roboticsengineering.in/encoder-counts-per-wheel-distance-calculator/) and [stepper frequency calculator](https://roboticsengineering.in/stepper-motor-step-frequency-calculator/).

## Signals and communication

- Period = 1 / frequency. A 50 Hz servo signal repeats every 20 ms.
- Typical hobby servo pulse: about 1 ms to 2 ms inside that 20 ms period, which is 5 to 10 percent duty. Check your servo’s datasheet for its real range.
- Serial speed: at 9600 baud with 8 data bits, no parity and 1 stop bit, each byte takes 10 bits, so about 960 bytes per second at most.
- Sampling: sample at more than twice the fastest change you need to see, and filter before you sample.

See the [servo pulse and PWM calculator](https://roboticsengineering.in/servo-pulse-width-pwm-calculator/).

## Use these responsibly

Formulas give an estimate, not a guarantee. Real motors have friction, batteries sag under load and parts vary. Measure on your own robot, keep a margin, and read the datasheet of every part. The [tools hub](https://roboticsengineering.in/tools/) lists every calculator, and the [Learn hub](https://roboticsengineering.in/learn/) explains the ideas behind them.

Last reviewed: November 2026. Free to copy and adapt for your own project, with credit. Written, checked and maintained by [Jignesh Panchal](https://www.linkedin.com/in/jignesh-s-panchal/) of [Jaadu Digital](https://jaadudigital.com/). See the [editorial standard](https://roboticsengineering.in/editorial-standard/).