[ { "name": "Temperature converter", "description": "Example of simple formula, just unit conversion", "input": [ {"name": "Input", "unit": "Kelvin" } ], "output": {"name": "Output", "unit": "Kelvin" }, "d4rtCode": "Output = Input;", "tags": ["converter", "temperature" ] }, // Free fall distance (vertical) { "name": "Free Fall Distance", "description": r""" Calculates vertical displacement under constant gravity $$h = \\frac{1}{2}gt^2$$ Where: - $g$: Gravitational acceleration ($9.81\\ \\mathrm{m/s^2}$ on Earth) - $t$: Time in free fall (seconds) ![Free Fall Diagram](https://altcalculator.com/wp-content/uploads/2023/08/Free-Fall.png)""", "input": [ {"name": "t", "unit": "second"}, // Time in seconds {"name": "g", "unit": "meters per second"} // Gravitational acceleration ], "output": {"name": "h", "unit": "meter"}, // Height in meters "d4rtCode": "h = 0.5 * g * pow(t, 2);", "tags": ["physics", "kinematics"] }, // Newton's Law of Universal Gravitation { "name": "Gravitational Force", "description": r''' Newton's law of universal gravitation \(F = G\\frac{m_1m_2}{r^2}\) Where: - $G$: Gravitational constant ($6.674\\times 10^{-11}\\ \\mathrm{N\\cdot m^2/kg^2}$) - $m_1, m_2$: Masses of two objects - $r$: Distance between centers of masses ![Gravitation](https://upload.wikimedia.org/wikipedia/commons/thumb/3/33/NewtonsLawOfUniversalGravitation.svg/1200px-NewtonsLawOfUniversalGravitation.svg.png)''', "input": [ {"name": "m1", "unit": "kilogram"}, // Mass 1 {"name": "m2", "unit": "kilogram"}, // Mass 2 {"name": "r", "unit": "meter"} // Distance between masses ], "output": {"name": "F", "unit": "newton"}, // Force in newtons "d4rtCode": "F = (6.67430e-11 * m1 * m2) / pow(r, 2);", "tags": ["physics", "astronomy", "gravity"] }, // Kinetic Energy { "name": "Kinetic Energy", "description": r''' Energy possessed by a moving object $$KE = \\frac{1}{2}mv^2$$ Where: - $m$: Mass of object - $v$: Velocity of object ![Kinetic Energy](https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Kinetic_energy.svg/1200px-Kinetic_energy.svg.png)''', "input": [ {"name": "m", "unit": "kilogram"}, // Mass {"name": "v", "unit": "meters per second"} // Velocity ], "output": {"name": "KE", "unit": "joule"}, // Energy in joules "d4rtCode": "KE = 0.5 * m * pow(v, 2);", "tags": ["physics", "energy", "mechanics"] }, // Projectile Motion Range { "name": "Projectile Range", "description": r"""Calculates horizontal distance of projectile motion $$R = \\frac{v^2 \\sin(2\\theta)}{g}$$ Where: - $v$: Initial velocity - $\\theta$: Launch angle - $g$: Gravitational acceleration ![Projectile Motion](https://upload.wikimedia.org/wikipedia/commons/thumb/5/52/Projectile_motion_diagram.png/800px-Projectile_motion_diagram.png)""", "input": [ {"name": "v", "unit": "meters per second"}, // Initial velocity {"name": "a", "unit": "degree"} // Launch angle ], "output": {"name": "R", "unit": "meter"}, // Horizontal distance "d4rtCode": """ var radians = a * (pi / 180); R = (pow(v, 2) * sin(2 * radians)) / 9.80665; """, "tags": ["physics", "kinematics", "projectile"] }, { "name": "Newton's Second Law", "description": r''' Force equals mass times acceleration $$F = m \\cdot a$$ Where: - $m$: Mass of object ($\\mathrm{kg}$) - $a$: Acceleration ($\\mathrm{m/s^2}$) ![Newton's Second Law](https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Newtonslawsofmotion.jpg/800px-Newtonslawsofmotion.jpg)''', "input": [ {"name": "m", "unit": "kilogram"}, // Mass {"name": "a", "unit": "meters per square second"} // Acceleration ], "output": {"name": "F", "unit": "newton"}, // Force in newtons "d4rtCode": "F = m * a;", "tags": ["physics", "mechanics", "newton"] }, // Apgar Score { "name": "Apgar Score", "description": "Newborn health assessment scoring system\n\nScores 0-2 for:\n1. Heart rate\n2. Breathing\n3. Muscle tone\n4. Reflexes\n5. Skin color\nTotal score 0-10", "input": [ {"name": "HeartRate", "values": ["Absent", "< 100 bpm>", "> 100 bpm"] }, {"name": "Breathing", "values": ["Absent", "Weak, irregular", "Strong, robust cry"] }, {"name": "MuscleTone", "values": ["None", "Some", "Flexed arms/leg, resists extension"] }, {"name": "Reflexes", "values": ["No response", "Grimace on aggressive stimulation", "Cry on stimulation"] }, {"name": "SkinColor", "values": ["Blue or pale", "Blue extremities, pink body", "Pink"] } ], "output": {"name": "Result", "unit": "string"}, "d4rtCode": """ var total = indexOf("HeartRate") + indexOf("Breathing") + indexOf("MuscleTone") + indexOf("Reflexes") + indexOf("SkinColor"); late var interpretation; if( total < 4 ) { interpretation = 'Critical condition'; } else if( total < 7 ){ interpretation = 'Needs assistance'; } else { interpretation = 'Normal'; } Result = 'Score: \$total - \$interpretation'; """, "tags": ["medical", "pediatrics", "assessment"] } , { "name": "Compare price per mass", "description": "Compares two products by their price per mass and returns which is cheaper, including price per kg for each product.", "input": [ {"name": "price1", "unit": "currency"}, {"name": "mass1", "unit": "kilogram"}, {"name": "price2", "unit": "currency"}, {"name": "mass2", "unit": "kilogram"} ], "output": {"name": "Result", "unit": "string"}, "d4rtCode": """ var p1 = price1 / mass1; var p2 = price2 / mass2; if (p1 < p2) { Result = 'first product is cheaper at \${p1.toStringAsFixed(2)} currency/kg vs \${p2.toStringAsFixed(2)} currency/kg'; } else if (p2 < p1) { Result = 'second product is cheaper at \${p2.toStringAsFixed(2)} currency/kg vs \${p1.toStringAsFixed(2)} currency/kg'; } else { Result = 'both products have the same price per mass at \${p1.toStringAsFixed(2)} currency/kg'; } """, "tags": ["comparison", "shopping", "economics"] } , // Einstein's Mass-Energy Equivalence { "name": "Mass-Energy Equivalence", "description": r''' Einstein's famous equation showing the relationship between mass and energy $$E = mc^2$$ Where: - $E$: Energy (Joules) - $m$: Mass (kilograms) - $c$: Speed of light ($299,792,458\\ \\mathrm{m/s}$) This equation shows that mass can be converted to energy and vice versa.''', "input": [ {"name": "m", "unit": "kilogram"} // Mass ], "output": {"name": "E", "unit": "joule"}, // Energy "d4rtCode": "E = m * pow(299792458, 2);", "tags": ["physics", "relativity", "energy"] }, // Ohm's Law { "name": "Ohm's Law", "description": r''' Relationship between voltage, current, and resistance in electrical circuits $$V = IR$$ Where: - $V$: Voltage (Volts) - $I$: Current (Amperes) - $R$: Resistance (Ohms) This fundamental law describes how current flows through resistive materials.''', "input": [ {"name": "I", "unit": "ampere"}, // Current {"name": "R", "unit": "ohm"} // Resistance ], "output": {"name": "V", "unit": "volt"}, // Voltage "d4rtCode": "V = I * R;", "tags": ["physics", "electricity", "electronics"] }, // Hooke's Law { "name": "Hooke's Law", "description": r''' Force exerted by a spring is proportional to its displacement $$F = -kx$$ Where: - $F$: Restoring force (Newtons) - $k$: Spring constant (N/m) - $x$: Displacement from equilibrium (meters) The negative sign indicates the force opposes the displacement.''', "input": [ {"name": "k", "unit": "newton per meter"}, // Spring constant {"name": "x", "unit": "meter"} // Displacement ], "output": {"name": "F", "unit": "newton"}, // Force "d4rtCode": "F = -k * x;", "tags": ["physics", "elasticity", "oscillations"] }, // Centripetal Force { "name": "Centripetal Force", "description": r''' Force required to keep an object moving in circular motion $$F = \\frac{mv^2}{r}$$ Where: - $F$: Centripetal force (Newtons) - $m$: Mass of object (kilograms) - $v$: Velocity (m/s) - $r$: Radius of circular path (meters) This force acts toward the center of the circle.''', "input": [ {"name": "m", "unit": "kilogram"}, // Mass {"name": "v", "unit": "meters per second"}, // Velocity {"name": "r", "unit": "meter"} // Radius ], "output": {"name": "F", "unit": "newton"}, // Force "d4rtCode": "F = (m * pow(v, 2)) / r;", "tags": ["physics", "circular motion", "centripetal"] }, // Wave Equation { "name": "Wave Equation", "description": r''' Relationship between wave speed, frequency, and wavelength $$v = f\\lambda$$ Where: - $v$: Wave speed (m/s) - $f$: Frequency (Hertz) - $\lambda$: Wavelength (meters) This applies to all types of waves including sound and light.''', "input": [ {"name": "f", "unit": "hertz"}, // Frequency {"name": "lambda", "unit": "meter"} // Wavelength ], "output": {"name": "v", "unit": "meters per second"}, // Wave speed "d4rtCode": "v = f * lambda;", "tags": ["physics", "waves", "frequency"] }, // Pythagorean Theorem { "name": "Pythagorean Theorem", "description": r''' Fundamental relation in Euclidean geometry among the three sides of a right triangle $$a^2 + b^2 = c^2$$ Where: - $a$, $b$: Legs of the right triangle - $c$: Hypotenuse of the right triangle The square of the hypotenuse is equal to the sum of squares of the other two sides.''', "input": [ {"name": "a", "unit": "meter"}, // First leg {"name": "b", "unit": "meter"} // Second leg ], "output": {"name": "c", "unit": "meter"}, // Hypotenuse "d4rtCode": "c = sqrt(pow(a, 2) + pow(b, 2));", "tags": ["trigonometry", "geometry", "pythagorean"] }, // Sine Rule { "name": "Sine Rule", "description": r''' Relationship between the sides and angles of any triangle $$\\frac{a}{\\sin A} = \\frac{b}{\\sin B} = \\frac{c}{\\sin C}$$ Where: - $a$, $b$, $c$: Sides of the triangle - $A$, $B$, $C$: Angles opposite to sides $a$, $b$, $c$ respectively This rule is useful for solving triangles when certain combinations of angles and sides are known.''', "input": [ {"name": "a", "unit": "meter"}, // Side a {"name": "A", "unit": "degree"}, // Angle A in degrees {"name": "B", "unit": "degree"} // Angle B in degrees ], "output": {"name": "b", "unit": "meter"}, // Side b "d4rtCode": """ var angleARad = A * (pi / 180); var angleBRad = B * (pi / 180); b = (a * sin(angleBRad)) / sin(angleARad); """, "tags": ["trigonometry", "triangle", "sine"] }, // Cosine Rule { "name": "Cosine Rule", "description": r''' Generalization of the Pythagorean theorem for any triangle $$c^2 = a^2 + b^2 - 2ab\\cos(C)$$ Where: - $a$, $b$, $c$: Sides of the triangle - $C$: Angle opposite to side $c$ This rule relates all three sides of a triangle to one of its angles.''', "input": [ {"name": "a", "unit": "meter"}, // Side a {"name": "b", "unit": "meter"}, // Side b {"name": "C", "unit": "degree"} // Angle C in degrees ], "output": {"name": "c", "unit": "meter"}, // Side c "d4rtCode": """ var angleCRad = C * (pi / 180); c = sqrt(pow(a, 2) + pow(b, 2) - 2*a*b*cos(angleCRad)); """, "tags": ["trigonometry", "triangle", "cosine"] }, // Trigonometric Identity { "name": "Trigonometric Identity", "description": r''' Fundamental Pythagorean identity in trigonometry $$\\sin^2(\\theta) + \\cos^2(\\theta) = 1$$ Where: - $\theta$: Any angle in radians or degrees This identity is derived from the Pythagorean theorem applied to the unit circle.''', "input": [ {"name": "theta", "unit": "degree"} // Angle in degrees ], "output": {"name": "result", "unit": "scalar"}, // Result (should be 1) "d4rtCode": """ var thetaRad = theta * (pi / 180); result = pow(sin(thetaRad), 2) + pow(cos(thetaRad), 2); """, "tags": ["trigonometry", "identity", "sine", "cosine"] } ]