Ultimate Math Conversion Cheat Sheet: 40+ Categories
This comprehensive guide covers mathematical conversions across all major fields - from basic measurements to advanced engineering and scientific formulas. Bookmark this page for quick reference!
1. Length / Distance
| Unit | Conversion |
|---|
| 1 kilometer (km) | = 1000 meters (m) |
| 1 meter (m) | = 100 centimeters (cm) |
| 1 centimeter (cm) | = 10 millimeters (mm) |
| 1 inch | = 2.54 centimeters (cm) |
| 1 foot (ft) | = 12 inches = 0.3048 meters |
| 1 yard (yd) | = 3 feet = 0.9144 meters |
| 1 mile | = 1760 yards = 1.609 kilometers |
| 1 nautical mile | = 1.852 kilometers |
2. Mass / Weight
| Unit | Conversion |
|---|
| 1 kilogram (kg) | = 1000 grams (g) |
| 1 gram (g) | = 1000 milligrams (mg) |
| 1 tonne (t) | = 1000 kilograms |
| 1 pound (lb) | = 16 ounces = 0.4536 kilograms |
| 1 ounce (oz) | = 28.35 grams |
| 1 stone | = 14 pounds = 6.35 kilograms |
3. Capacity / Volume
| Unit | Conversion |
|---|
| 1 liter (L) | = 1000 milliliters (mL) |
| 1 cubic meter (m³) | = 1000 liters |
| 1 gallon (UK) | = 4.546 liters |
| 1 gallon (US) | = 3.785 liters |
| 1 quart (US) | = 0.946 liters |
| 1 pint (US) | = 0.473 liters |
| 1 fluid ounce (US) | = 29.57 milliliters |
4. Time
| Unit | Conversion |
|---|
| 1 minute | = 60 seconds |
| 1 hour | = 60 minutes = 3600 seconds |
| 1 day | = 24 hours |
| 1 week | = 7 days |
| 1 month (average) | ≈ 30.44 days |
| 1 year | = 12 months = 365 days (366 in leap year) |
5. Temperature
| Conversion | Formula |
|---|
| Celsius → Fahrenheit | (°C × 9/5) + 32 |
| Fahrenheit → Celsius | (°F − 32) × 5/9 |
| Celsius → Kelvin | °C + 273.15 |
| Kelvin → Celsius | K − 273.15 |
6. Currency (Approximate)
| Conversion | Example (as of 2025) |
|---|
| 1 USD | ≈ 83 INR |
| 1 EUR | ≈ 90 INR |
| 1 GBP | ≈ 104 INR |
Note: Always check live rates for exact conversions.
7. Area
| Unit | Conversion |
|---|
| 1 square meter (m²) | = 10.7639 square feet |
| 1 square kilometer (km²) | = 100 hectares = 1,000,000 m² |
| 1 hectare | = 10,000 m² |
| 1 acre | = 4046.86 m² |
| 1 square mile | = 2.59 km² |
| 1 square foot | = 144 square inches = 0.0929 m² |
8. Speed
| Unit | Conversion |
|---|
| 1 kilometer per hour (km/h) | = 0.2778 meters/second (m/s) |
| 1 meter/second (m/s) | = 3.6 km/h |
| 1 mile per hour (mph) | = 1.609 km/h |
| Speed of light | = 3 × 10⁸ m/s |
9. Energy / Power
| Unit | Conversion |
|---|
| 1 joule (J) | = 1 newton-meter (N·m) |
| 1 kilojoule (kJ) | = 1000 joules |
| 1 calorie | = 4.184 joules |
| 1 kilocalorie (kcal) | = 4184 joules |
| 1 watt (W) | = 1 joule/second |
| 1 kilowatt (kW) | = 1000 watts |
| 1 horsepower (hp) | = 746 watts |
10. Pressure
| Unit | Conversion |
|---|
| 1 pascal (Pa) | = 1 N/m² |
| 1 kilopascal (kPa) | = 1000 Pa |
| 1 bar | = 100,000 Pa |
| 1 atmosphere (atm) | = 101,325 Pa |
| 1 mmHg | = 133.3 Pa |
11. Angles
| Unit | Conversion |
|---|
| 1 degree (°) | = 60 minutes (′) |
| 1 minute (′) | = 60 seconds (″) |
| 1 radian | = 57.2958 degrees |
| 1 degree | = π/180 radians |
12. Data Storage
| Unit | Conversion |
|---|
| 1 byte | = 8 bits |
| 1 kilobyte (KB) | = 1024 bytes |
| 1 megabyte (MB) | = 1024 KB |
| 1 gigabyte (GB) | = 1024 MB |
| 1 terabyte (TB) | = 1024 GB |
13. Force
| Unit | Conversion |
|---|
| 1 newton (N) | = 1 kg·m/s² |
| 1 dyne | = 10⁻⁵ newton |
| 1 kilogram-force (kgf) | = 9.80665 newtons |
| 1 pound-force (lbf) | = 4.44822 newtons |
14. Astronomy / Space Units
| Unit | Conversion |
|---|
| 1 astronomical unit (AU) | = 149,597,870.7 kilometers |
| 1 light-year | = 9.461 × 10¹² kilometers |
| 1 parsec (pc) | = 3.086 × 10¹³ kilometers |
| 1 solar mass (M☉) | = 1.989 × 10³⁰ kilograms |
15. Electricity & Magnetism
| Unit | Conversion |
|---|
| 1 coulomb (C) | = 1 ampere-second (A·s) |
| 1 volt (V) | = 1 joule/coulomb |
| 1 ohm (Ω) | = 1 volt/ampere |
| 1 farad (F) | = 1 coulomb/volt |
| 1 henry (H) | = 1 ohm·second |
| 1 tesla (T) | = 1 weber/m² |
| 1 kilowatt-hour (kWh) | = 3.6 × 10⁶ joules |
16. Density & Specific Gravity
| Unit | Conversion |
|---|
| Density (ρ) | = mass/volume |
| 1 g/cm³ | = 1000 kg/m³ |
| Water's density | = 1 g/cm³ = 1000 kg/m³ |
| Specific gravity | = (density of substance) / (density of water) |
17. Frequency & Wavelength
| Unit | Conversion |
|---|
| 1 hertz (Hz) | = 1 cycle/second |
| 1 kilohertz (kHz) | = 1000 Hz |
| 1 megahertz (MHz) | = 10⁶ Hz |
| 1 gigahertz (GHz) | = 10⁹ Hz |
| Wavelength (λ) | = Speed of light / Frequency |
18. Geometry – Common Formula Conversions
| Shape | Formula |
|---|
| Area of square | = side² |
| Area of rectangle | = length × breadth |
| Area of triangle | = ½ × base × height |
| Area of circle | = πr² |
| Circumference of circle | = 2πr |
| Volume of cube | = side³ |
| Volume of cuboid | = length × breadth × height |
| Volume of cylinder | = πr²h |
| Volume of sphere | = (4/3)πr³ |
| Volume of cone | = (1/3)πr²h |
19. Trigonometric Conversions
| Conversion | Formula |
|---|
| sin²θ + cos²θ | = 1 |
| tanθ | = sinθ / cosθ |
| secθ | = 1 / cosθ |
| cosecθ | = 1 / sinθ |
| cotθ | = 1 / tanθ = cosθ / sinθ |
| tan(90°−θ) | = cotθ |
| sin(90°−θ) | = cosθ |
20. Logarithmic & Exponential Conversions
| Conversion | Formula |
|---|
| logₐb | = ln(b) / ln(a) |
| aˣ = b | ⇒ logₐb = x |
| log₁₀(1) | = 0 |
| log₁₀(10) | = 1 |
| ln(e) | = 1 |
| ln(1) | = 0 |
| eˣ | = antilog (ln x) |
21. Financial Mathematics
| Concept | Formula |
|---|
| Simple Interest | SI = (P × R × T) / 100 |
| Compound Interest | A = P(1 + R/100)ⁿ |
| Discount | = Marked Price − Selling Price |
| Profit % | = (Profit / Cost Price) × 100 |
| Loss % | = (Loss / Cost Price) × 100 |
22. Number System Conversions
| Conversion | Formula / Rule |
|---|
| Binary → Decimal | Multiply each bit by 2ⁿ (from right) |
| Decimal → Binary | Divide by 2, record remainders |
| Octal → Decimal | Multiply each digit by 8ⁿ |
| Hexadecimal → Decimal | Multiply each digit by 16ⁿ |
| 1 byte | = 8 bits |
23. Momentum & Energy
| Unit | Conversion |
|---|
| Momentum (p) | = mass × velocity (kg·m/s) |
| Kinetic Energy | = ½mv² |
| Potential Energy | = mgh |
| Work done | = Force × Distance |
24. Flow & Pressure
| Unit | Conversion |
|---|
| Flow rate | = Volume / Time |
| 1 liter/second | = 0.001 m³/s |
| 1 bar | = 10⁵ pascals |
| 1 psi | = 6894.76 pascals |
25. Miscellaneous / Useful Constants
| Constant | Value |
|---|
| π (pi) | = 3.14159265 |
| e (Euler's number) | = 2.7182818 |
| g (gravity on Earth) | = 9.80665 m/s² |
| c (speed of light) | = 3 × 10⁸ m/s |
| Avogadro's number | = 6.022 × 10²³ mol⁻¹ |
| Planck's constant | = 6.626 × 10⁻³⁴ Js |
| Universal gas constant (R) | = 8.314 J/mol·K |
26. Torque & Rotational Motion
| Unit | Conversion |
|---|
| Torque (τ) | = Force × Distance |
| 1 newton-meter (N·m) | = 1 joule per radian |
| 1 pound-foot (lb·ft) | = 1.35582 N·m |
| Angular velocity (ω) | = 2π × frequency |
| 1 revolution per minute (rpm) | = 2π/60 radians per second |
27. Navigation & Geography
| Unit | Conversion |
|---|
| 1 degree (°) of latitude | ≈ 111 km |
| 1 minute (′) of latitude | ≈ 1.85 km |
| 1 knot | = 1 nautical mile per hour = 1.852 km/h |
| Bearing angle | Measured clockwise from North |
| Longitude difference | Time difference × 15° per hour |
28. Chemistry & Mole Conversions
| Concept | Conversion |
|---|
| 1 mole | = 6.022 × 10²³ particles |
| Molar mass | = mass (g) / moles |
| 1 mol gas (STP) | = 22.4 liters |
| % purity | = (Pure substance / Total sample) × 100 |
| ppm (parts per million) | = (mass of solute / mass of solution) × 10⁶ |
29. Statistics & Probability Conversions
| Concept | Formula |
|---|
| Mean (x̄) | = Σx / n |
| Variance (σ²) | = Σ(x − x̄)² / n |
| Standard Deviation (σ) | = √Variance |
| Probability | = Favourable outcomes / Total outcomes |
| Permutation | = nPr = n! / (n−r)! |
| Combination | = nCr = n! / [r!(n−r)!] |
30. Coordinate Geometry
| Concept | Formula |
|---|
| Distance between points | = √((x₂−x₁)² + (y₂−y₁)²) |
| Midpoint | = ((x₁+x₂)/2, (y₁+y₂)/2) |
| Slope (m) | = (y₂−y₁)/(x₂−x₁) |
| Equation of line | y = mx + c |
| Circle equation | (x−h)² + (y−k)² = r² |
31. Thermodynamics
| Concept | Conversion |
|---|
| 1 calorie | = 4.184 joules |
| 1 BTU (British thermal unit) | = 1055.06 joules |
| 1 horsepower-hour | = 2.685 × 10⁶ joules |
| Specific heat (c) | = Q / (mΔT) |
| Gas constant (R) | = 8.314 J/mol·K |
32. Light & Optics
| Concept | Conversion |
|---|
| Refractive index (n) | = c / v |
| 1 lumen | = 1 candela·steradian |
| 1 lux | = 1 lumen/m² |
| Focal length (f) | = 1 / (1/v + 1/u) |
| Magnification | = image height / object height |
33. Sound & Acoustics
| Concept | Conversion |
|---|
| Speed of sound (air) | ≈ 343 m/s |
| Frequency | = 1 / Time period |
| Intensity level (dB) | = 10 × log₁₀(I / I₀) |
| 1 bel | = 10 decibels |
| Wavelength | = velocity / frequency |
34. Gravitation & Planetary Motion
| Concept | Conversion |
|---|
| Gravitational force | F = Gm₁m₂ / r² |
| Acceleration due to gravity | g = GM / R² |
| Escape velocity | = √(2GM / R) |
| Orbital velocity | = √(GM / r) |
| G (universal constant) | = 6.674 × 10⁻¹¹ N·m²/kg² |
35. Matrix & Vector Conversions
| Concept | Formula |
|---|
| Vector magnitude | = √(x² + y² + z²) |
| Dot product | A·B = |A||B|cosθ |
| Cross product | A×B = |A||B|sinθ·n |
| Determinant (2×2) | = ad − bc |
| Determinant (3×3) | = a(ei−fh) − b(di−fg) + c(dh−eg) |
36. Differential Calculus
| Concept | Formula |
|---|
| Derivative of xⁿ | = n·xⁿ⁻¹ |
| d/dx(sin x) | = cos x |
| d/dx(cos x) | = −sin x |
| d/dx(eˣ) | = eˣ |
| Chain Rule | = dy/dx = (dy/du) × (du/dx) |
| Product Rule | = (uv)' = u'v + uv' |
| Quotient Rule | = (u/v)' = (u'v − uv') / v² |
37. Integral Calculus
| Concept | Formula |
|---|
| ∫xⁿ dx | = (xⁿ⁺¹)/(n+1) + C |
| ∫1/x dx | = ln|x| + C |
| ∫eˣ dx | = eˣ + C |
| ∫sin x dx | = −cos x + C |
| ∫cos x dx | = sin x + C |
| ∫sec²x dx | = tan x + C |
38. Business Math / Ratio & Proportion
| Concept | Formula |
|---|
| Ratio | = a : b |
| Proportion | a/b = c/d |
| Partnership profit share | = (Capital × Time) of each partner |
| Average | = (Sum of terms) / (Number of terms) |
| Percentage | = (Part / Whole) × 100 |
39. Construction / Civil Conversions
| Conversion | Formula |
|---|
| 1 cubic meter cement | ≈ 1440 kg |
| 1 cubic meter sand | ≈ 1600 kg |
| 1 cubic meter brick masonry | ≈ 500 bricks (standard size) |
| 1 psi | = 0.0703 kg/cm² |
| 1 N/mm² | = 10.1972 kg/cm² |
40. Heat & Cooling
| Conversion | Formula |
|---|
| °C to °F | (°C × 9/5) + 32 |
| °F to °C | (°F − 32) × 5/9 |
| Kelvin to °C | K − 273.15 |
| Latent heat | = Q / m |
| Specific heat | = Q / (mΔT) |
Conclusion
This comprehensive math conversion guide covers essential formulas and conversions across mathematics, physics, engineering, statistics, commerce, astronomy, computer science, and more. Bookmark this page for quick reference during studies, work, or exam preparation!
