Smart Math Formula Calculator

Algebraic Formulas

1. (a + b)² = a² + 2ab + b²
2. (a - b)² = a² - 2ab + b²
3. (a + b)(a - b) = a² - b²
4. a³ + b³ = (a + b)(a² - ab + b²)
5. (x + a)(x + b) = x² + (a + b)x + ab
6. (x + a)(x - a) = x² - a²
7. (a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc
8. x² = (x + a)(x - a)
9. a² - b² = (a + b)(a - b)
10. a³ - b³ = (a - b)(a² + ab + b²)
11. a⁴ - b⁴ = (a² + b²)(a² - b²)
12. a² + 2ab + b² = (a + b)²
13. a² - 2ab + b² = (a - b)²
14. (x + y)(x - y) = x² - y²
15. (x + y)² = x² + y² + 2xy
16. a + b + c = 0, a = -b - c
17. x = (-b ± √(b² - 4ac)) / 2a
18. a = b / c
19. (a + b)³ = a³ + 3a²b + 3ab² + b³
20. a² + b² = c² (Pythagorean Theorem)
21. x² + y² = r² (Circle Equation)
22. ax + by + c = 0 (Linear Equation)
23. a * (x + y) = ax + ay
24. (a + b) * (a - b) = a² - b²
25. aⁿ * aᵐ = aⁿ⁺ᵐ

Trigonometric Formulas

1. sin²(θ) + cos²(θ) = 1
2. tan(θ) = sin(θ) / cos(θ)
3. sin(2θ) = 2sin(θ)cos(θ)
4. cos(2θ) = cos²(θ) - sin²(θ)
5. tan(2θ) = (2tan(θ)) / (1 - tan²(θ))
6. sin(θ) = opposite / hypotenuse
7. cos(θ) = adjacent / hypotenuse
8. tan(θ) = opposite / adjacent
9. sec(θ) = 1 / cos(θ)
10. cosec(θ) = 1 / sin(θ)
11. cot(θ) = 1 / tan(θ)
12. sin(90° - θ) = cos(θ)
13. cos(90° - θ) = sin(θ)
14. tan(90° - θ) = cot(θ)
15. sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
16. cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
17. tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
18. sin²(θ) = (1 - cos(2θ)) / 2
19. cos²(θ) = (1 + cos(2θ)) / 2
20. tan²(θ) = (1 - cos(2θ)) / (1 + cos(2θ))
21. cot²(θ) = (1 + cos(2θ)) / (1 - cos(2θ))
22. sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
23. cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
24. tan(A - B) = (tan(A) - tan(B)) / (1 + tan(A)tan(B))
25. sin(θ) = 1 / csc(θ)

Parameter Formulas

1. Perimeter of Rectangle = 2(l + w)
2. Perimeter of Square = 4s
3. Perimeter of Circle = 2πr
4. Perimeter of Triangle = a + b + c
5. Area of Rectangle = l × w
6. Area of Square = s²
7. Area of Circle = πr²
8. Area of Triangle = 1/2 × b × h
9. Area of Rhombus = 1/2 × d1 × d2
10. Area of Trapezium = 1/2 × (a + b) × h
11. Volume of Cube = s³
12. Volume of Rectangular Box = l × w × h
13. Volume of Cylinder = πr²h
14. Volume of Sphere = 4/3πr³
15. Volume of Cone = 1/3πr²h
16. Surface Area of Cube = 6s²
17. Surface Area of Rectangular Box = 2lw + 2lh + 2wh
18. Surface Area of Cylinder = 2πr² + 2πrh
19. Surface Area of Sphere = 4πr²
20. Surface Area of Cone = πr(r + l)
21. Perimeter of Parallelogram = 2(a + b)
22. Perimeter of Ellipse = 2π√[(a² + b²)/2]
23. Perimeter of Regular Polygon = n × side
24. Lateral Surface Area of Cylinder = 2πrh
25. Lateral Surface Area of Cone = πrl

Geometry Formulas

1. Area of Triangle = 1/2 × b × h
2. Perimeter of Circle = 2πr
3. Volume of Sphere = 4/3πr³
4. Volume of Cone = 1/3πr²h
5. Area of Rectangle = l × w
6. Surface Area of Sphere = 4πr²
7. Surface Area of Cylinder = 2πr² + 2πrh
8. Volume of Cylinder = πr²h
9. Surface Area of Cone = πr(r + l)
10. Perimeter of Square = 4s
11. Volume of Rectangular Box = l × w × h
12. Surface Area of Rectangular Box = 2lw + 2lh + 2wh
13. Area of Rhombus = 1/2 × d1 × d2
14. Area of Parallelogram = b × h
15. Pythagoras Theorem: a² + b² = c²
16. Euler's Formula for Polyhedra: V - E + F = 2
17. Area of Sector = (θ / 360) × πr²
18. Length of Arc = (θ / 360) × 2πr
19. Volume of Hemisphere = 2/3πr³
20. Surface Area of Hemisphere = 3πr²
21. Surface Area of Ellipsoid = 4π[(a² + b² + c²) / 3]
22. Volume of Ellipsoid = 4/3πabc
23. Surface Area of Elliptical Cylinder = 2πrh + 2πr²
24. Volume of Elliptical Cylinder = πr²h
25. Volume of Torus = 2π²r₁r₂²

Circle Formulas

1. Area of Circle = πr²
2. Circumference of Circle = 2πr
3. Diameter of Circle = 2r
4. Length of Arc = (θ / 360) × 2πr
5. Area of Sector = (θ / 360) × πr²
6. Area of Segment = Area of Sector - Area of Triangle
7. Perimeter of Circle = 2πr
8. Equation of Circle = x² + y² = r²
9. Circumference with Radius = 2πr
10. Circle Area with Radius = πr²