Is there / does anyone know of an equation to calculate a humanoid's jump height from jump power?

The JumpPower property defines the initial Y velocity of the character when the jump is activated. This then comes down to rather basic physics. I set up a little ugly experiment that can give quite accurate results.

local player = game.Players.LocalPlayer
local character = player.Character or player.CharacterAdded:Wait()
local humanoid = character:WaitForChild("Humanoid")

humanoid.Jumping:Connect(function()
	--	First calculate the time it takes to reach the peak of the jump (v = Vector3.new() so we can exclude it)
	--	v = v0 + at
	local v0 = Vector3.new(0, humanoid.JumpPower, 0)
	local a = -workspace.Gravity
	local t = (v0 / -a).Y

	--	Caclulate the final position
	--	x = x0 + v0*t + (1/2)*a*t^2
	a = Vector3.new(0, a, 0)
	local x0 = character.PrimaryPart.Position
	local v0 = character.PrimaryPart.Velocity
	local x = x0 + v0*t + (1/2)*a*t^2
	print("EXPECTED", x)


	local tab = {}
	local startPos = character.PrimaryPart.Position
	local connection = game:GetService("RunService").Heartbeat:Connect(function()
		tab[#tab + 1] = character.PrimaryPart.Position.Y - startPos.Y
	end)
	wait(t*2)
	connection:Disconnect()
	print("PEAKED AT", startPos + Vector3.new(0, math.max(unpack(tab)), 0))
end)

Forgot to mention; the Jumping event for some reason fires twice and it first does the calculations with incorrect values. But this should point you to the right direction.

To calculate the required JumpPower to reach a certain height, you can first calculate the potential energy (mgh) which when the jump starts is turned into kinetic energy ((1/2)mv^2). From there you can solve for v, which is the required velocity. You can also use this to calculate the height if you know the JumpPower.

local player = game.Players.LocalPlayer
local character = player.Character or player.CharacterAdded:Wait()
local humanoid = character:WaitForChild("Humanoid")

local part = workspace.Part

local g = workspace.Gravity
local m = 0 do
	for _, part in next, character:GetDescendants() do
		if part:IsA("BasePart") then
			m = m + part:GetMass()
		end
	end
end

humanoid.Jumping:Connect(function()
	--	potential energy = kinetic energy
	--	mgh = (1/2)*m*v^2
	--	solve for v
	local footPos = character.PrimaryPart.Position - Vector3.new(0, 2, 0)
	--	 Keep in mind this example only works for parts that are standing straight. You can use pythagorean to find the height of tilted parts.
	local h = (part.Position + Vector3.new(0, part.Size.Y/2, 0) - footPos).Y
	local v = math.sqrt(2) * (math.sqrt(m * m*g*h) / m)
	humanoid.JumpPower = v
end)