Calculate the final velocity and height of an object in free fall using our Free Fall Calculator. Perfect for physics students, teachers, and enthusiasts.
Enter any three inputs to calculate the other two values
How to use this Free Fall Calculator 🤔
There are input fields for Initial velocity \((u)\), Time of fall \((t)\), Acceleration due to gravity \((g)\), Final velocity \((v)\), and Height \((h)\). Enter any three inputs to calculate the other two values.
The calculator uses the \( v = u + g \cdot t \) \( h = u \cdot t + \frac{1}{2} g \cdot t^2 \) formula, substitues given values, and calcuates the missing value.
The missing value is calcuated and displayed in the input field. Also, the caculation is displayed under the input section.
What is Free Fall?
Free fall refers to the motion of an object falling under the influence of gravity alone, without any air resistance. The key parameters in free fall are time of fall (t), final velocity (v), height (h), initial velocity (u), and the acceleration due to gravity (g).
Calculating Final Velocity and Height
The final velocity of an object in free fall is calculated using the formula:
\( v = u + g \cdot t \).
The height from which the object falls is calculated using the formula:
{
"topic": "free-fall",
"input_types": [
"float",
"float",
"float",
"float",
"float"
],
"input_labels": [
"u",
"t",
"g",
"v",
"h"
],
"input_descriptions": [
"Initial velocity",
"Time of fall",
"Acceleration due to gravity",
"Final velocity",
"Height"
],
"element_string": " of object",
"input_units": [
"m/s",
"s",
"m/s²",
"m/s",
"m"
],
"input_values": [
"0",
"",
"9.81",
"",
""
],
"formula_mathjax": "\\( v = u + g \\cdot t \\)<br>\\( h = u \\cdot t + \\frac{1}{2} g \\cdot t^2 \\)",
"input_pre_msg": "Enter any three inputs to calculate the other two values",
"type": "Calculate",
"title": "Free Fall Calculator",
"description": "Calculate the final velocity and height of an object in free fall using our Free Fall Calculator. Perfect for physics students, teachers, and enthusiasts.",
"category": "Kinematics",
"template": "physics",
"precision": 10,
"formulas": [
{
"parameters": [
"t",
"u",
"g"
],
"outputs": [
{
"label": "v",
"formula": " u + g * t ",
"formula_mathjax": "\\( u + g \\cdot t \\)",
"formula_mathjax_sub": "\\( u + g \\times t \\)"
},
{
"label": "h",
"formula": " u * t + 0.5 * g * Math.pow( t , 2 ) ",
"formula_mathjax": "\\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)",
"formula_mathjax_sub": "\\( u \\times t + \\frac{1}{2} \\times g \\times t ^2 \\)"
}
],
"example_heading": "Consider that a person dropped an object from the top of a building with an initial velocity of _u_. The object travelled for _t_ before touching the ground.<br>What is the final velocity of object, and height of the building?",
"examples": [
{
"t": 10,
"u": 4,
"g": 9.81
},
{
"t": 2,
"u": 0,
"g": 9.81
}
]
},
{
"parameters": [
"v",
"u",
"g"
],
"outputs": [
{
"label": "t",
"formula": " ( v - u ) / g ",
"formula_mathjax": "\\( \\frac{ v - u }{ g } \\)"
},
{
"label": "h",
"formula": " u * ( v - u ) / g + 0.5 * g * Math.pow( ( v - u ) / g , 2 ) ",
"formula_mathjax": "\\( u \\cdot \\frac{ v - u }{ g } + \\frac{1}{2} g \\cdot \\left( \\frac{ v - u }{ g } \\right)^2 \\)",
"formula_mathjax_sub": "\\( u \\times \\frac{ v - u }{ g } + \\frac{1}{2} \\times g \\times \\left( \\frac{ v - u }{ g } \\right)^2 \\)"
}
],
"example_heading": "Consider that a bird dropped a toy from top of an electric pole. The initial velocity of the toy is _u_. The toy reached a final velocity of _v_ before touching the ground.<br>What is the height of the pole, and time taken by the toy to reach the ground?",
"examples": [
{
"v": 20,
"u": 4,
"g": 9.81
}
]
},
{
"parameters": [
"h",
"u",
"g"
],
"outputs": [
{
"label": "t",
"formula": " ( - u + Math.sqrt( Math.pow( u , 2 ) + 2 * g * h ) ) / g ",
"formula_mathjax": "\\( \\frac{ - u + \\sqrt{ u ^2 + 2 g h } }{ g } \\)",
"formula_mathjax_sub": "\\( \\frac{ - u + \\sqrt{ u ^2 + 2 \\times g \\times h } }{ g } \\)"
},
{
"label": "v",
"formula": " Math.sqrt( Math.pow( u , 2 ) + 2 * g * h ) ",
"formula_mathjax": "\\( \\sqrt{ u ^2 + 2 g h } \\)",
"formula_mathjax_sub": "\\( \\sqrt{ u ^2 + 2 \\times g \\times h } \\)"
}
],
"example_heading": "Consider that a bird dropped chicken lollipop from top of a building of height _h_. Since, the bird slipped it, consider that initial velocity is _u_.<br>Calculate the time taken by the chicken lollipop to reach ground, and also its final velocity with which it makes contact with ground.",
"examples": [
{
"h": 50,
"u": 0,
"g": 9.81
}
]
},
{
"parameters": [
"v",
"t",
"g"
],
"outputs": [
{
"label": "u",
"formula": " v - g * t ",
"formula_mathjax": "\\( v - g \\cdot t \\)",
"formula_mathjax_sub": "\\( v - g \\times t \\)"
},
{
"label": "h",
"formula": " ( v - g * t ) * t + 0.5 * g * Math.pow( t , 2 ) ",
"formula_mathjax": "\\(( v - g \\cdot t ) \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)",
"formula_mathjax_sub": "\\(( v - g \\times t ) \\times t + \\frac{1}{2} \\times g \\times t ^2 \\)"
}
],
"example_heading": "The same bird throwed another chicken lollipop from top of another building. Consider that we somehow calculated the final velocity to be _v_, time to reach the ground to be _t_. <br>Calculate the initial velocity of the chicken lollipop with which the bird has thrown it, and also height of the building.",
"examples": [
{
"t": 5,
"v": 50,
"g": 9.81
}
]
},
{
"parameters": [
"h",
"t",
"g"
],
"outputs": [
{
"label": "u",
"formula": " ( h - 0.5 * g * Math.pow( t , 2 ) ) / t ",
"formula_mathjax": "\\( \\frac{ h - \\frac{1}{2} g \\cdot t ^2 }{ t } \\)",
"formula_mathjax_sub": "\\( \\frac{ h - \\frac{1}{2} \\times g \\times t ^2 }{ t } \\)"
},
{
"label": "v",
"formula": " ( h + 0.5 * g * Math.pow( t , 2 ) ) / t ",
"formula_mathjax": "\\( \\frac{ h + \\frac{1}{2} g \\cdot t^2 }{ t } \\)",
"formula_mathjax_sub": "\\( \\frac{ h + \\frac{1}{2} \\times g \\times t ^2 }{ t } \\)"
}
]
},
{
"parameters": [
"h",
"v",
"g"
],
"outputs": [
{
"label": "t",
"formula": " ( v + Math.sqrt( Math.round( ( v * v - 2 * g * h ) * 100) / 100 ) ) / g ",
"formula_mathjax": "\\( \\frac{ v + \\sqrt{ v ^2 - 2 g h } }{ g } \\)",
"formula_mathjax_sub": "\\( \\frac{ v + \\sqrt{ v ^2 - 2 \\times g \\times h } }{ g } \\)"
},
{
"label": "u",
"formula": " v - g * t ",
"formula_mathjax": "\\( v - g \\cdot t \\)",
"formula_mathjax_sub": "\\( v - g \\times t \\)"
}
]
},
{
"parameters": [
"t",
"u",
"h"
],
"outputs": [
{
"label": "g",
"formula": " ( 2 * ( h - u * t ) ) / Math.pow( t , 2 ) ",
"formula_mathjax": "\\( \\frac{ 2 \\cdot ( h - u \\cdot t ) }{ t ^2 } \\)",
"formula_mathjax_sub": "\\( \\frac{ 2 \\times ( h - u \\times t ) }{ t ^2 } \\)"
},
{
"label": "v",
"formula": " u + g * t ",
"formula_mathjax": "\\( u + g \\cdot t \\)",
"formula_mathjax_sub": "\\( u + g \\times t \\)"
}
]
}
],
"content": "<h2>What is Free Fall?</h2><p>Free fall refers to the motion of an object falling under the influence of gravity alone, without any air resistance. The key parameters in free fall are time of fall (t), final velocity (v), height (h), initial velocity (u), and the acceleration due to gravity (g).</p><h2>Calculating Final Velocity and Height</h2><p>The <strong>final velocity</strong> of an object in free fall is calculated using the formula:</p><p class=\"formula_highlite\">\\( v = u + g \\cdot t \\).</p><p>The <strong>height</strong> from which the object falls is calculated using the formula:</p><p class=\"formula_highlite\">\\( h = u \\cdot t + \\frac{1}{2} g \\cdot t^2 \\).</p>"
}
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