Scientific Calculator Formulas

Comprehensive reference guide for all mathematical formulas you need

This page provides a comprehensive reference of mathematical formulas organized by category. Use our calculator above to compute these formulas quickly and accurately.

Algebra Formulas

Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Solves quadratic equations of the form ax² + bx + c = 0. The discriminant (b² - 4ac) determines the nature of roots.
Difference of Squares
a² - b² = (a + b)(a - b)
Factoring formula for the difference of two perfect squares.
Perfect Square Trinomial
(a + b)² = a² + 2ab + b²
Expansion of a binomial squared. Also works with subtraction: (a - b)² = a² - 2ab + b².
Sum and Product of Roots
Sum = -b/a, Product = c/a
For quadratic equation ax² + bx + c = 0, sum and product of roots α and β.
Arithmetic Sequence
aₙ = a₁ + (n-1)d
nth term of arithmetic sequence where a₁ is first term and d is common difference.
Geometric Sequence
aₙ = a₁ · r^(n-1)
nth term of geometric sequence where a₁ is first term and r is common ratio.

Trigonometry Formulas

Pythagorean Identity
sin²θ + cos²θ = 1
Fundamental trigonometric identity relating sine and cosine.
Tangent Identity
tan θ = sin θ / cos θ
Definition of tangent in terms of sine and cosine.
Sine Sum Formula
sin(A + B) = sin A cos B + cos A sin B
Sum formula for sine function. For difference: sin(A - B) = sin A cos B - cos A sin B.
Cosine Sum Formula
cos(A + B) = cos A cos B - sin A sin B
Sum formula for cosine function. For difference: cos(A - B) = cos A cos B + sin A sin B.
Double Angle Formula (Sine)
sin 2θ = 2 sin θ cos θ
Double angle formula for sine function.
Double Angle Formula (Cosine)
cos 2θ = cos²θ - sin²θ
Double angle formula for cosine. Also equals 2cos²θ - 1 or 1 - 2sin²θ.
Law of Sines
a/sin A = b/sin B = c/sin C
Relates sides and angles in any triangle. Used for solving non-right triangles.
Law of Cosines
c² = a² + b² - 2ab cos C
Generalizes Pythagorean theorem for any triangle. Useful for finding unknown sides or angles.

Logarithm Formulas

Product Rule
log(xy) = log x + log y
Logarithm of a product equals sum of logarithms.
Quotient Rule
log(x/y) = log x - log y
Logarithm of a quotient equals difference of logarithms.
Power Rule
log(xⁿ) = n · log x
Logarithm of a power equals exponent times logarithm.
Change of Base Formula
log_b(x) = log(x) / log(b)
Converts logarithm to any base using common (base 10) logarithms.
Natural Logarithm Base
ln(e) = 1
Natural logarithm of e equals 1. Also: ln(1) = 0.
Exponential-Logarithm Relationship
e^(ln x) = x
Exponential and logarithm are inverse functions. Also: ln(e^x) = x.

Geometry Formulas

Circle Area
A = πr²
Area of circle where r is radius. Use π ≈ 3.14159.
Circle Circumference
C = 2πr
Circumference (perimeter) of circle where r is radius.
Sphere Volume
V = (4/3)πr³
Volume of sphere where r is radius.
Sphere Surface Area
A = 4πr²
Surface area of sphere where r is radius.
Cylinder Volume
V = πr²h
Volume of cylinder where r is radius and h is height.
Cone Volume
V = (1/3)πr²h
Volume of cone where r is base radius and h is height.
Triangle Area
A = (1/2)bh
Area of triangle where b is base and h is height.
Heron's Formula
A = √(s(s-a)(s-b)(s-c))
Triangle area from side lengths a, b, c where s = (a+b+c)/2 is semi-perimeter.

Statistics Formulas

Mean (Average)
μ = Σx / n
Arithmetic mean where Σx is sum of all values and n is count.
Variance
σ² = Σ(x - μ)² / n
Population variance measuring spread from mean μ.
Standard Deviation
σ = √(Σ(x - μ)² / n)
Standard deviation is square root of variance, measuring data spread.
Permutations
P(n,r) = n! / (n-r)!
Number of ways to arrange r items from n items where order matters.
Combinations
C(n,r) = n! / (r!(n-r)!)
Number of ways to choose r items from n items where order doesn't matter.
Probability
P(A) = favorable / total
Basic probability formula: favorable outcomes divided by total possible outcomes.

Common Physics Formulas

Distance Formula
d = vt
Distance equals velocity times time (constant velocity).
Acceleration Formula
a = (v - u) / t
Acceleration equals change in velocity divided by time.
Kinetic Energy
KE = (1/2)mv²
Kinetic energy where m is mass and v is velocity.
Potential Energy
PE = mgh
Gravitational potential energy where m is mass, g is gravity (9.8 m/s²), h is height.
Force (Newton's Second Law)
F = ma
Force equals mass times acceleration.
Power Formula
P = W / t
Power equals work done divided by time. Also P = E/t for energy.

How to Use These Formulas

These formulas are essential tools for students and professionals working with mathematics, science, and engineering. Our scientific calculator supports all the operations needed to compute these formulas quickly and accurately.

To use a formula, simply identify the values you know, substitute them into the formula, and use the calculator to perform the necessary operations. Remember to use parentheses to ensure the correct order of operations, especially when dealing with complex expressions involving multiple operations.

For detailed explanations of how to use the calculator for specific types of calculations, visit our How to Use page. For practical examples and tutorials, check out our blog section.